This post by Donald is relevant here.
My votes are, like many of those here, just as much about the theme of the set as the power of the cards. Chapel is super-strong, but it's at its best when there's an engine to be had, and there usually isn't in base set. And, no, I'm not including any of the base cards in my calcuation here, no Platinum/Colony/Potion.
Base:
Smithy and
Witch. The base set is all about simplicity, and Smithy is in a very real sense the simplest card in the game (even if Harem has less text).
Intrigue:
Masquerade,
Nobles, and probably either
Torturer or
Minion. In addition to the stated Victory theme and the choices theme (the latter of which all of these cards have), Intrigue is definitely the cruelest expansion. Nobles has to be the most typical- it's the one Victory card that actually gives you a choice- but how can you leave out Masq? Most other sets only have one or two easy choices, but I think it's fitting that I can't decide for Intrigue.
Seaside:
Tactician. Nothing else comes close, this is a pure "your next turn" card way above and beyond all the other Durations- and luckily enough it's one of the strongest cards of the set too. (Wharf is the typical #1 choice but I think it's pretty close actually). For all its overwhelming strength, Ambassador is too off-theme to be counted here.
Alchemy:
Scrying Pool and
Vineyard. Alchemy is all about Potions, and also "caring about Actions", and these are the two Potion cards which care the most about Actions. Conveniently enough they're also the second and third-best cards in the set.
Prosperity:
King's Court. Nothing else is bigger and badder. Goons, Grand Market, and Bank are all fine runners-up, touching on some of the sub-themes that KC doesn't (VP chips and Treasure). Goons may very well be the strongest card in all of Dominion, in fact, I think its only competition is KC and Ambassador (2-player games only).
Cornucopia:
Tournament, with a runner-up prize to
all of them 'cause it's about variety har har. Actually not really, the runner-up is
Menagerie. I'm really surprised that Tournament hasn't been mentioned more here; it's arguably the set's strongest card (though probably second to Hunting Party), and nothing else does more for variety, by putting five new unique cards in the game. Apparently it was the superstar in playtesting, too. Menagerie gets the runner-up nod for integrating the old hand management sub-theme. Hunting Party is probably the set's best card, but it leads to too many HP spam games where lack of variety is the goal.
Hinterlands:
Ill-Gotten Gains,
Embassy, and
Tunnel. Donald X has identified a bunch of themes within Hinterlands beyond just "when gain" abilities- there's a lot of sifting, alternate Victory and Reactions, and in general a whole turn towards decks which are fat (esp. with Silver), and which can deal with their enlarged size well. IGG is of course the quintessential game-warping when-gain card, Embassy is another strong card which uses the when-gain as a nerf instead, and also ties into sifting, Tunnel is a Victory-Reaction! (which gets better with sifting around), 'nuff said.
Promo: Gotta be
Black Market.