Base: Smithy
Most people so far have said Village. I don't really agree. Smithy is the easiest card in the game to understand, and usually the first one I explain when I teach the game to people - you draw 3 cards. That's it. Plus, it's good in Big Money AND engines, not just in engines (like Village), and we all know Base was pretty money-centered compared to the expansions.
Intrigue: Nobles
Intrigue has a lot of alt-VP and a lot of cards with choices. Nobles is the only one that's both.
Seaside: Lighthouse
Seaside introduces Durations, so it should definitely be a Duration. But which one? I could say Wharf, but that would be the third terminal draw card in a row, and Wharf might be strong, but its ability is not that exciting or Seaside-defining. Lighthouse, on the other hand, might be the strongest defensive card in the game, which is important in an expansion with a couple of brutal attacks. It cleverly uses the Duration mechanics, and on top of it all, no other card fits better in Seaside thematically.
Alchemy: Alchemist
Yeah, it's another draw card, but it costs Potion, uses the Potion later on, and is named directly after the expansion itself.
Prosperity: King's Court
It's expensive, it's strong, it's perfect for the 'bigger and better' theme: it's a bigger and better version of Throne Room in all possible ways. I would have chosen Goons, because it also uses the victory tokens, but goons are hardly ever prosperous, so thematically it wouldn't make a lot of sense...
Cornucopia: Horn of Plenty
It likes variety, which is the main theme, and thematically it kinda defines the expansion.
Hinterlands: Noble Brigand
Hinterlands contains a lot of 'fixes' for the base set, and Noble Brigand fixes some of the issues with Thief very well (although, of course, it is still not extremely strong). It has also an on-buy effect, which is one of the main themes of Hinterlands.
Dark Ages: Rats
It's a card that's difficult to use, it has an on-trash effect (which is Dark Ages' main theme), and it's Donald's favorite card so it deserves some mention as a 'face of Dominion'. Oh, and there were a lot of rats in the dark ages, which caused a lot of trouble, so it's extremely thematic too.
Guilds: Merchant Guild
It has Guild in its game and it gives coin tokens, one of the main themes. Too bad there's no card that has both an overpay effect and something with coin tokens.
Adventures: Peasant
Definitely either an Event or one of the two Travellers - I chose a Traveller because Events are not considered cards. The Peasant goes on an actual adventure (moreso than the Page, who just becomes stronger), and then eventually becomes a Teacher, which uses all of the +1 tokens, another important part of the set.
Promo: Black Market
Clearly most suitable as a promo. Its rules are very quirky, it requires a lot of setup, it's a lot of fun but also high-variance.
All of Dominion: Jack of All Trades
It's one of the most versatile cards, showing off various important possibilities in Dominion: gaining, trashing, drawing and deck-ordering.
