A fun overall game!
Single-Player: You get your most known modes: Grand Prix, and Time Trials along with two more. Single-Player versions of VS and Battle. The Grand Prix is pretty solid, and as you advance through 50cc - Mirror Mode, you can see that there is difference between the difficulty. Time Trials is not the best again and mostly to find short cuts.
Multi-Player: As always, Mario Kart Wii is really great multi-player, you don't have as a wide as selection as in Double-Dash, but you have VS and Battle. The VS is fine with Wii and Retro courses, but as far as the Battle mode goes, you can't kill each other in 3 - 4 players. The Battle mode puts you on teams, either red or blue. You have Balloon Battle, but counts score not which team loses their players first. There is also Coin Runners where players must collect coins. Not much excitement there.
The game supports online play. Why play online play? For a large screen... just play on the same Wii console, you'll probably have more fun laughing with your friends, then laughing by yourself.
Mario Kart Wii gets a 9.0 out of 10.0 for having a magnificent multi-player and a single player that works well.