I haven't played it but you might want to try renting Cooking Mama. Seems that people like it, would be good for a couple. You could also try Excite Truck if you like racing.
Theres also Trauma Center: Second Opinion, where you do surgeries sort of. I hear it can be challenging though.
You can play super mario galaxy two player, but I hear its not so great 2 player.
I can't think of anything that has trivia persay. You might like playing Zack and Wiki together. It's a quality puzzle game, only single player but you can work the puzzles together.
I've seen Cranium Kabooki at the store, I haven't really heard anything about it. I assume it'd just be an extension of the board game sort of.
Theres also mercury meltdown revolution. It's supposedly a really great game for an affordable $20.