So, I'm defining Staple for the purposes of this discussion as a card one can usually expect to see played (with good reason) in decks of the associated color. Demonic Tutor, for example, should be and most likely is in any deck containing black in this format so I'd consider that to be a staple.
Some of the cards that are on my list are maybe controversial, people might disagree and so I encourage people to bring up cards that are not on the list that should be or maybe make a case for why one should be removed. Or maybe cards should be added. This thread is for discussing what cards are necessary for making a deck run efficiently.
White:
Faith's Fetters - Enchants any pernement, disables creatures and all activated abilities and randomly makes you not lose to burn.
Land Tax - Fixes mana, thins deck, and gives the white player excellent hand advantage, a strong move before armageddon.
Enlightened Tutor - Fetches Top, combo pieces, or a lot of good answers as an instant.
Swords to Plowshares - Removes almost anything from the game for W at no real gain to your opponent.
Wrath of God - Gives great card advantage when it kills multiple creatures, helps control to stabilize.
Armageddon - Prevents control from stabilizing, disables a lot of strong decks. Stops bombs from being played. Usually assures victory once you have a superior board position.
Ravages of War - A second chance at drawing Armageddon.
Decree of Justice Uncounterable "put X tokens into play" at instant speed, you may draw a card. An excellent control finisher. It isn't bad when hardcasted and is deadly with cards like mana drain.
Jotun Grunt - An aggressive creature that heckles decks trying to capitalize on their graveyard. Efficient against Loam, Mindslaver, things you suspect will be Regrown, genesis, gigapede, or feeding cards back into your library you can tutor for.
Exalted Angel - 4/5 Flying Lifelinker that can feasibly come out on the fourth turn. It's an unfair advantage in the damage race, is a good control finisher and is good at outracing control decks.
Austere Command - Probably the best 'bad' wrath of god. It's very versatile and frequently will be the answer you need.
Disenchant - I find 'disenchants' always have a worthwhile target in highlander games.
Mirror Entity - It's hard to build tribal in highlander, so this fills in a lot of gaps, being a changeling, and makes creatures that were weenies in the early game much bigger to finish the game.
Blue
Mana Drain - Steals a turn and a card out of their hand, and gives you mana to set up for a win on the next turn.
Fact or Fiction Because it only has one blue in the casting cost, decks that only use blue for splash can play this amazingly powerful hand and graveyard filler. There is almost never a way for an opponent to separate a fact or fiction that won't give you a ridiculous advantage.
Deep Analysis A draw spell that can be played twice, netting 4 cards.
Dissipate - Things like to come back from the graveyard in highlander, so this counterspell is almost necessary for anyone trying to use blue for control.
Cryptic Command - A hard counter/targeted removal/turn-stealer/cantrip.
Misdirection - Changes removal targets, throws uncountable burn spells and Mind Twist back at the caster's face, counters counterspells, retargets drawspells... it's a sneaky and important move in a format where blue cannot have four force of will.
Back to Basics - If you're mana base is in vast majority basic, punishing most of the format for playing mostly nonbasics is the thing to do. It's a one-sided stasis against 90% of highlander.
Treachery- Frequently a two-for-one, is also a win condition if you steal a good enough creature.
Bribery - Denies them their card, puts a bomb into play under your control.
Intuition A good tutor that gets a life from the loam engine online, dumps genesis, gigapede, or mindslaver, and is necessary for running reanimator.
Gifts Ungiven - Good for the same reasons intuition is.
Trinket Mage - Top, Engineered Explosives, Phyrexian Furnace, pithing needle, zuran orb, and cursed scroll are all strong targets for him in this format.
Capsize Can steal multiple turns, is often "blue vindicate."
Morphling - Strictly good as a control finisher, though he's a fundamental include for any blue-based control decks in that he's an excellent blocker, attacker, has evasion, and can't be targeted.
Thirst for Knowledge - An instant speed drawspell that is good in reanimator or decks with plenty of artifacts.
Personal Tutor - Wrath, Decree, Ancient Craving, Upheval, or some red X-spell are all good targets for this card in this format. Sadly, Mystical tutor is banned but this does its job.
Opportunity -Because games tend to be long in highlander, it's feasible to cast this at the end of an opponent's turn most games and really cannot be replaced by any other card as far as something that's going to significantly increase the number of cards in your hand as an instant- Maybe stroke of Genius, however, Opportunity is cheaper costed at six.
Black:
Demonic Tutor - It's not banned yet!
Damnation - Another Wrath of God
Phyrexian Negator - Most highlander decks are too slow to handle this card.
Chainer's Edict - Removal you can play twice!
Entomb - Tutors for anything that's good in your graveyard, can be comboed with Regrowth. Necessary in reanimator.
Duress - Disrupts control, takes important burn spells, spot removal, or combo pieces.
Thoughtsieze - Good for the same reasons Duress is.
Skeletal Scrying - A really efficient instant-speed draw spell.
Withered Wretch - A low-cost threat that disrupts graveyards, good for the same reasons Jotun Grunt is.
Stinkweed Imp - Its deathtouch makes it kill things that might not be killable with spells or activated abilities or wraths, and it comes back from the dead, dumping goodies into your graveyard as it does.
Unearth A sneaky thing to do in an aggro deck, I think. It also reanimates some really big creatures like Psychatog, terravore, or tarmogoyf. Can cycle if unneeded.
Mind Twist - A really good disruption spell that just got unbanned! Watch out for misdirection.
Red:
Grim Lavamancer - Recurring burn that can come out early.
Shattering Pulse - Recurring artifact destruction. It always has a target in highlander.
Ruination - Played for the same reason Back to Basics is.
Magus of the Moon - Played for the same reason Back to Basics is.
Blood Moon - Another nonbasic hoser.
Price of Progress - A really good game finisher in this format.
Banefire - Uncounterable X damage.
Demonfire - Uncounterable X damage.
Rolling Earthquake - Red wrath of god that deals X damage.
Goblin Welder - Combos with mindslaver, sundering titan, Smokestacks, and other silly artifacts that destroy one's opponent.
Viashino Heretic - Recurring artifact destruction that deals punishes the artifact's controller and is a small threat.
Countryside Crusher - helps you draw into burn, and he gets really big real fast.
Kird Ape - Too good for any red/green aggro deck not to play.
Pillage - There are a lot of artifacts and lands that need to be destroyed, like Maze of ith, Tabernacle, Library, Masticore, and vedalken shackles. Because it's versatile I think any red deck can play it, lando or not.
Green:
Llanowar Elves/fyndhorn elves - Puts you a turn ahead manawise, and is a creature threat.
Birds of Paradise - Another card that sets you a turn ahead.
Regrowth - Lets you play any effect multiple times.
All Sun's Dawn - Gives excellent hand advantage of quality cards.
Eternal Witness - Played for the same reason regrowth is.
Krosan Grip - Uncounterable disenchant effect.
Mirri's Guile - Played for the same reason Sensei's Divining Top is.
Garruk Wildspeaker - Can untap gaea's cradle, constantly produce threats, and overrun for the kill. Essentially costs 2 because of its first ability.
Call of the Herd - A threat you can play twice.
Life From the Loam - Recurs wasteland, is a draw engine with the cycling lands, and dredges important graveyard-based cards.
Gigapede - Cannot be maze of ithed, is not a worthwhile bribery target, cannot be thwarted with counterspells, and forces opponents to sacrifice creatures with they attack or block. Is strong with life from the loam and intuition.
Sylvan Library - Played for the same reason top is, improving green's consistency and giving hand advantage the color usually does not have.
Genesis - Constantly recurs creature threats from your graveyard.
Crop Rotation - Fetches Library, forbidden orchard, maze of ith, bazaar of baghdad, wasteland, dustbowl, tabernacle, or fixes your mana.
Desert Twister - In decks without black/white, the cost of desert twister is well worth the while of its caster for "destroy target pernement." Mono green does not have many ways of killing creatures apart from this and bad abilities like deathtouch. I see this card get played to good effect and is often a necessary draw for the decks that run it.
Multicolor
Pernicious Deed - The most efficient wrath spell in Magic, it will stop you from losing to aggro.
Army Ants - For three, this creature turns any of your lands into strip mine.
Psychatog - It's been a format wrecker in every MTG format since it was printed, and highlander is no exception. He's a terrific early game blocker and late game he's a three-costed phaige the untouchable. When he's untapped, he's Moat, when he's tapped, he's the Abyss. Any deck loaded with draw spells and protection should capitalize on this card.
Fire/Ice - either a two-for-one or a turn-stealer.
Vindicate - Well, I tried to make a case for Desert Twister. However, this is clearly the best card that "destroys target permanent."
Stormbind - It turns cards into damage, which, when aggro decks go on topdeck, this card is good for all the reasons cursed scroll is.
Figure of Destiny a one-drop that catches up with the pace of the game as you pay mana. Is a strong threat at any point in the game.
Putrefy - Instant-speed burial of any creature, or artifact destruction. Kills Swords or mana accelerators.
Mortify Instant-speed burial of any creature, or enchantment removal. Removes faith's fetters, sylvan library, or other obnoxious enchantments.
Lim-Dul's Vault The format does not have Vampiric Tutor, so this is the next best thing.
Hull Breach - A disenchant with a possible two-for-one.
Terminate - Buries any creature.
Artifact
Sensei's Divining Top
Oblivion Stone
Fellwar Stone
Mind Stone
Coalition Relic
Sword of Fire and Ice
Sword of Light and Shadow
Phyrexian Furnace
Engineered Explosives
Scroll Rack
Crucible of Worlds
Masticore
Land:
Library of Alexandria
Mishra's Workshop
Bazaar of Baghdad
Tolaria West
Onslaught Fetches
Mirage Fetches
Krosan Visage
Manlands
Karakas
Maze of Ith
Thawing Glaciers
Dust bowl
Wasteland
Reflecting Pool
*Edit: Definitions added, "yavimya ants" changed to "army ants"
Some of the cards that are on my list are maybe controversial, people might disagree and so I encourage people to bring up cards that are not on the list that should be or maybe make a case for why one should be removed. Or maybe cards should be added. This thread is for discussing what cards are necessary for making a deck run efficiently.
White:
Faith's Fetters - Enchants any pernement, disables creatures and all activated abilities and randomly makes you not lose to burn.
Land Tax - Fixes mana, thins deck, and gives the white player excellent hand advantage, a strong move before armageddon.
Enlightened Tutor - Fetches Top, combo pieces, or a lot of good answers as an instant.
Swords to Plowshares - Removes almost anything from the game for W at no real gain to your opponent.
Wrath of God - Gives great card advantage when it kills multiple creatures, helps control to stabilize.
Armageddon - Prevents control from stabilizing, disables a lot of strong decks. Stops bombs from being played. Usually assures victory once you have a superior board position.
Ravages of War - A second chance at drawing Armageddon.
Decree of Justice Uncounterable "put X tokens into play" at instant speed, you may draw a card. An excellent control finisher. It isn't bad when hardcasted and is deadly with cards like mana drain.
Jotun Grunt - An aggressive creature that heckles decks trying to capitalize on their graveyard. Efficient against Loam, Mindslaver, things you suspect will be Regrown, genesis, gigapede, or feeding cards back into your library you can tutor for.
Exalted Angel - 4/5 Flying Lifelinker that can feasibly come out on the fourth turn. It's an unfair advantage in the damage race, is a good control finisher and is good at outracing control decks.
Austere Command - Probably the best 'bad' wrath of god. It's very versatile and frequently will be the answer you need.
Disenchant - I find 'disenchants' always have a worthwhile target in highlander games.
Mirror Entity - It's hard to build tribal in highlander, so this fills in a lot of gaps, being a changeling, and makes creatures that were weenies in the early game much bigger to finish the game.
Blue
Mana Drain - Steals a turn and a card out of their hand, and gives you mana to set up for a win on the next turn.
Fact or Fiction Because it only has one blue in the casting cost, decks that only use blue for splash can play this amazingly powerful hand and graveyard filler. There is almost never a way for an opponent to separate a fact or fiction that won't give you a ridiculous advantage.
Deep Analysis A draw spell that can be played twice, netting 4 cards.
Dissipate - Things like to come back from the graveyard in highlander, so this counterspell is almost necessary for anyone trying to use blue for control.
Cryptic Command - A hard counter/targeted removal/turn-stealer/cantrip.
Misdirection - Changes removal targets, throws uncountable burn spells and Mind Twist back at the caster's face, counters counterspells, retargets drawspells... it's a sneaky and important move in a format where blue cannot have four force of will.
Back to Basics - If you're mana base is in vast majority basic, punishing most of the format for playing mostly nonbasics is the thing to do. It's a one-sided stasis against 90% of highlander.
Treachery- Frequently a two-for-one, is also a win condition if you steal a good enough creature.
Bribery - Denies them their card, puts a bomb into play under your control.
Intuition A good tutor that gets a life from the loam engine online, dumps genesis, gigapede, or mindslaver, and is necessary for running reanimator.
Gifts Ungiven - Good for the same reasons intuition is.
Trinket Mage - Top, Engineered Explosives, Phyrexian Furnace, pithing needle, zuran orb, and cursed scroll are all strong targets for him in this format.
Capsize Can steal multiple turns, is often "blue vindicate."
Morphling - Strictly good as a control finisher, though he's a fundamental include for any blue-based control decks in that he's an excellent blocker, attacker, has evasion, and can't be targeted.
Thirst for Knowledge - An instant speed drawspell that is good in reanimator or decks with plenty of artifacts.
Personal Tutor - Wrath, Decree, Ancient Craving, Upheval, or some red X-spell are all good targets for this card in this format. Sadly, Mystical tutor is banned but this does its job.
Opportunity -Because games tend to be long in highlander, it's feasible to cast this at the end of an opponent's turn most games and really cannot be replaced by any other card as far as something that's going to significantly increase the number of cards in your hand as an instant- Maybe stroke of Genius, however, Opportunity is cheaper costed at six.
Black:
Demonic Tutor - It's not banned yet!
Damnation - Another Wrath of God
Phyrexian Negator - Most highlander decks are too slow to handle this card.
Chainer's Edict - Removal you can play twice!
Entomb - Tutors for anything that's good in your graveyard, can be comboed with Regrowth. Necessary in reanimator.
Duress - Disrupts control, takes important burn spells, spot removal, or combo pieces.
Thoughtsieze - Good for the same reasons Duress is.
Skeletal Scrying - A really efficient instant-speed draw spell.
Withered Wretch - A low-cost threat that disrupts graveyards, good for the same reasons Jotun Grunt is.
Stinkweed Imp - Its deathtouch makes it kill things that might not be killable with spells or activated abilities or wraths, and it comes back from the dead, dumping goodies into your graveyard as it does.
Unearth A sneaky thing to do in an aggro deck, I think. It also reanimates some really big creatures like Psychatog, terravore, or tarmogoyf. Can cycle if unneeded.
Mind Twist - A really good disruption spell that just got unbanned! Watch out for misdirection.
Red:
Grim Lavamancer - Recurring burn that can come out early.
Shattering Pulse - Recurring artifact destruction. It always has a target in highlander.
Ruination - Played for the same reason Back to Basics is.
Magus of the Moon - Played for the same reason Back to Basics is.
Blood Moon - Another nonbasic hoser.
Price of Progress - A really good game finisher in this format.
Banefire - Uncounterable X damage.
Demonfire - Uncounterable X damage.
Rolling Earthquake - Red wrath of god that deals X damage.
Goblin Welder - Combos with mindslaver, sundering titan, Smokestacks, and other silly artifacts that destroy one's opponent.
Viashino Heretic - Recurring artifact destruction that deals punishes the artifact's controller and is a small threat.
Countryside Crusher - helps you draw into burn, and he gets really big real fast.
Kird Ape - Too good for any red/green aggro deck not to play.
Pillage - There are a lot of artifacts and lands that need to be destroyed, like Maze of ith, Tabernacle, Library, Masticore, and vedalken shackles. Because it's versatile I think any red deck can play it, lando or not.
Green:
Llanowar Elves/fyndhorn elves - Puts you a turn ahead manawise, and is a creature threat.
Birds of Paradise - Another card that sets you a turn ahead.
Regrowth - Lets you play any effect multiple times.
All Sun's Dawn - Gives excellent hand advantage of quality cards.
Eternal Witness - Played for the same reason regrowth is.
Krosan Grip - Uncounterable disenchant effect.
Mirri's Guile - Played for the same reason Sensei's Divining Top is.
Garruk Wildspeaker - Can untap gaea's cradle, constantly produce threats, and overrun for the kill. Essentially costs 2 because of its first ability.
Call of the Herd - A threat you can play twice.
Life From the Loam - Recurs wasteland, is a draw engine with the cycling lands, and dredges important graveyard-based cards.
Gigapede - Cannot be maze of ithed, is not a worthwhile bribery target, cannot be thwarted with counterspells, and forces opponents to sacrifice creatures with they attack or block. Is strong with life from the loam and intuition.
Sylvan Library - Played for the same reason top is, improving green's consistency and giving hand advantage the color usually does not have.
Genesis - Constantly recurs creature threats from your graveyard.
Crop Rotation - Fetches Library, forbidden orchard, maze of ith, bazaar of baghdad, wasteland, dustbowl, tabernacle, or fixes your mana.
Desert Twister - In decks without black/white, the cost of desert twister is well worth the while of its caster for "destroy target pernement." Mono green does not have many ways of killing creatures apart from this and bad abilities like deathtouch. I see this card get played to good effect and is often a necessary draw for the decks that run it.
Multicolor
Pernicious Deed - The most efficient wrath spell in Magic, it will stop you from losing to aggro.
Army Ants - For three, this creature turns any of your lands into strip mine.
Psychatog - It's been a format wrecker in every MTG format since it was printed, and highlander is no exception. He's a terrific early game blocker and late game he's a three-costed phaige the untouchable. When he's untapped, he's Moat, when he's tapped, he's the Abyss. Any deck loaded with draw spells and protection should capitalize on this card.
Fire/Ice - either a two-for-one or a turn-stealer.
Vindicate - Well, I tried to make a case for Desert Twister. However, this is clearly the best card that "destroys target permanent."
Stormbind - It turns cards into damage, which, when aggro decks go on topdeck, this card is good for all the reasons cursed scroll is.
Figure of Destiny a one-drop that catches up with the pace of the game as you pay mana. Is a strong threat at any point in the game.
Putrefy - Instant-speed burial of any creature, or artifact destruction. Kills Swords or mana accelerators.
Mortify Instant-speed burial of any creature, or enchantment removal. Removes faith's fetters, sylvan library, or other obnoxious enchantments.
Lim-Dul's Vault The format does not have Vampiric Tutor, so this is the next best thing.
Hull Breach - A disenchant with a possible two-for-one.
Terminate - Buries any creature.
Artifact
Sensei's Divining Top
Oblivion Stone
Fellwar Stone
Mind Stone
Coalition Relic
Sword of Fire and Ice
Sword of Light and Shadow
Phyrexian Furnace
Engineered Explosives
Scroll Rack
Crucible of Worlds
Masticore
Land:
Library of Alexandria
Mishra's Workshop
Bazaar of Baghdad
Tolaria West
Onslaught Fetches
Mirage Fetches
Krosan Visage
Manlands
Karakas
Maze of Ith
Thawing Glaciers
Dust bowl
Wasteland
Reflecting Pool
*Edit: Definitions added, "yavimya ants" changed to "army ants"