I LOVE Mario Kart!! It's amazing. Me and my friends played it pretty much the whole time while we were away, and I got everyone converted to using the controller with the nunchuck as opposed to the wheel- much more controlled steering that way.
Anyway, Mario Party is an awesome game. It's kind of like a board game- you throw the dice, move along the board, you get different bonuses, bad things happen, etc etc. You also get to do mini-games with other players, to try and score more points. It's very random and very fun!
Also, have you got WarioWare? That's great too. It is THE most random thing ever though. You have to master different 'moves' with the wii-mote, and then complete challenges with them. For instance. use the wii-mote as a broom, and then brush leaves away from a yard, as a crazy old lady character. The games are all very short, and once you complete it you unlock multi-player mode and you can play some great team games (before we unlocked the multi-player mode we just took it in turns to complete it).
I also got Steve Monopoly for his birthday which looks really good but we haven't managed to play it yet...