Power Nine

You are looking at over $100,000 of cardboard.

The Power Nine are the most powerful (and therefore expensive) cards in Magic: The Gathering, all first printed in Limited Edition Alpha, the original form of the game. Every single one of them is so broken that they are banned in every format except Vintage (a format that exists as an asylum for cards too powerful for the other formats) and even then they're restricted to one per deck. The first magic video game, commonly known as Shandalar, had a defacto ban on these cards: Unlike every other card in the game, the Power Nine can only be obtained as random treasure from high level dungeons and you might go through dozens without finding one.

The Cards

Ancestral Recall

Target player draws 3 cards.

That's three cards for one mana. If you're not immediately jizzing your pants at the thought of what you can do with that, you'll fit right in with the rest of /tg/ when it comes to Magic.

Black Lotus

Sacrifice Black Lotus: Add three mana of any one color to your mana pool.

Mother of god. Forget linear infinite mana, there are ways to go exponentially infinite mana with this. Wizards has a long history of trying to "fix" this card, and every time except for one (Lotus Bloom, which takes three turns to get you mana and still ended up being the highlight of at least one World Championship deck) the "balanced" Lotus clone was still so hideously broken that it ended up getting banned.

Moxen

Five artifacts, each imitating a basic land.

This is a big deal because while basic lands are restricted to one per turn to keep endgame from happening by turn three, artifacts have no such restriction; you can play them all at once to get your heavy hitters on the board while your opponent is still playing with two-drops. This was even worse when the Moxen were originally printed, because at that time there was no restriction on the number of duplicate cards in your deck. You could replace all your basic lands with Moxen with no downside other than the time and money required to get the cards.

Time Walk

Take an extra turn after this one.

There have been many ways to take an extra turn in Magic, but this is and will always be the cheapest and least restrictive way to do it. This makes it trivial to set up a combo that lets you play the same Time Walk over and over again for infinite turns. In fact, for a while the sheer infamy of this card led to the DCI banning all cards of the form "take an extra turn after this one" from non-Vintage formats because of the distorting effect of infinite-turns combos, and all the extra-turn cards Wizards prints of late generally either have punishing preconditions or make you lose the game after the end of the extra turn.

Timetwister

Each player shuffles his or her hand and graveyard into his or her library, then draws seven cards.

Timetwister isn't as obviously broken as the other members of the Power Nine, since it's seemingly symmetrical, but if there's a large asymmetry in players' current hand sizes the casting player can get a downright degenerate level of card swing out of one card and three mana, while kicking any combo pieces out of the opponents' hands and/or graveyards. Timetwister has the unique distinction of being the only member of the Power Nine not banned/restricted in every format; it's legal in Commander, though its expense and rarity means you're very unlikely to see it (and frankly in Commander there's a good chance you'll regret giving your opponent a fresh hand).

Additional Contenders

A few cards have been called the tenth member of the Power Nine, but they have never been officially adopted as such because they were not ridiculously broken.

Contract from Below

Discard your hand, ante the top card of your library, and draw 7 cards. Remove contract from below from your deck at the beginning of the game if you're not playing for ante.

Literally banned from every format not because of its power level but because it incorporates literal gambling into the game. WotC banned it, alongside all other ante cards before the authorities would step in because the game had gambling elements. Ignoring the fact that it adds to your ante, it lets you draw a whole new hand for a single black mana. You are probably not losing if you just drew a whole new hand, and if this card can be built around (like in a storm deck) it is downright unstoppable. But again, since it is an ante card it cannot be legally used in any official format. Since Shandalar is a single-player video game the gambling problem isn't relevant and even then it's on the same defacto ban list as the Power Nine.

Library of Alexandria

{T}: Add {1} to your mana pool.
{T}: Draw a card. Activate this ability only if you have exactly seven cards in hand.

More mana is always nice, but the second ability is what really makes this card. The extra drawing power might seem limited at first, but when you combine it with additional drawing power from any source this card becomes valuable in just about any deck that draws cards. This is so powerful that Library of Alexandria is Restricted in Vintage and Banned everywhere else.

Sol Ring

{T}: Add {2} to your mana pool.

Sol Ring is a ridiculous mana source from Alpha that is restricted in Vintage, which leads many to refer to it as the tenth member of the Power Nine, although Library of Alexandria is also a strong contender for the title. Unlike the "real" Power Nine, Sol Ring is weak enough to be considered legal in Commander, where the increased life totals and singleton limit on cards keep the ramp it provides from being too big of a deal.

Tolarian Academy

{T}: Add {U} to your mana pool for each artifact you control.

HAHAHAHAHAHAHAHAHAHA. Banned. Banned in Legacy, banned in Commander, restricted in Vintage. This legendary land doesn't even come into play tapped. It can pump more mana off the goddamn moxes and sol rings.