So okay, all Dominion cards are unique in that none of them are exactly the same as any others. But most of them are made up of more or less the same atoms, as Donald once put it: +cards, +actions, +buy, +$, +VP; discard, trash, reveal, set aside, gain, top-deck, look at; etc. But there are a few cards that do things unlike anything any other card does. Now that Hinterlands is out, several cards that were unique for a long time are no longer unique—Mint is obviously no longer the only card with an on-buy effect; thanks to Inn, Counting House is no longer the only card that allows you to remove cards from your discard pile. But there are new unique features to some of the cards in Hinterlands, and some of the unique features of other cards are still unique:
Ambassador is the only card that can return a card to the Supply.
Coppersmith is the only card that changes the effect of playing another card.
Duchess is the only card that changes the effect of gaining another card.
Embargo is the only card that changes the effect of buying another card.
Inn is the only card that allows you to shuffle your non-empty deck.
Masquerade is the only card that allows cards to be passed between players.
Outpost is the only card that changes how many cards you draw in cleanup.
Pearl Diver is the only card that causes you to interact with a card in your deck other than the top card.
Philosopher's Stone is the only card that allows you to count your discard pile.
Possession is the only card that allows one player to make decisions for another player's turn.
Stash is the only card that allows you to stack the deck while shuffling.
Tunnel is the only card sensitive to when something is being discarded.
Young Witch is the only card that changes the number of Kingdom piles in the game.
Are there any other cards with totally unique properties? Note that even some cards with oddball features, like Grand Market, have atoms that exist in other card properties. (Grand Market and Contraband both have effects that can forbid you from buying something; Grand Market and lots of other cards have effects that are sensitive to what is in play at the moment.) Note that I don't discriminate between what triggers the effects; in the case of Young Witch and Duchess, it's simply their presence in the game. What triggers an effect (on play, on buy, on gain, when in play, when present, etc.) is just another atom.