Many great one already mentioned:
Katamari
Wario Ware + Twisted
Portal
Devil Dice (only played Bombastic though)
Papers Please
also:
Starseed Pilgrim
It's more like a very clever twist on existing gameplay mechanics. A bit like Braid. I like how figuring out the rules is an integral part of the game itself.
Mario Party (esp. 3 for me)
Why was it never successfully copied?! Great combination of board and video game. The mix of action, stategy and luck goes so well together, unlike in later iterations or similar games.
Tamagochi
Seaman was mentioned. But a "game" that you cannot pause and you HAVE to carry with you all the time? It made you actually care. Amazing achievment.
Werewolf
That board/party game. Was very amazed how well the rules amplify role play, lies and treachery in a social and real life situation. I bet there are online versions of that game. But for me the true fun comes from the social interaction, the tone of the voice, body language (or pointing and screaming at each other). Don't know how old it actually is, but it's such a unique concept.
Mario Chase, Luigi's Ghost Mansion, AC: Sweet Day (Minigames from Nintendoland) and Fruit (Minigame from Game&Wario)
Asymmetric gameplay at it's best. So much fun that always takes the social situation into consideration. I love it.