There are really three big changes to Mario Kart Wii that makes it stand out from previous entries in the series, and most of them are for the better unlike Double Dash!!. The biggest addition to the franchise that actually has long lasting effects are the inclusion of bikes into races. When I first heard that bikes were being added to the series, I honestly could have cared less. I thought that it wouldn't give any significant change to the core game and was just there for aesthetic purposes. After playing though, man did I change my mind on that. Bikes are just plain fun to drive in. They're light, they have great acceleration, and I just prefer to drive in them. They even included tricks into races for both bikes and karts, where if you're able to pull one off you get a little speed boost, which is a fair way at equalizing the game.
Also, you obviously have the addition of motion controls to the series. Most copies of this game were bundled with the Wii Wheel to encourage people to play with the motion controls, but it supports Gamecube controllers, Wii classic controllers, and the Wii remote with nunchuk. There's plenty of variety for everyone to find a control scheme that works for me, my personal favorite being the Wii remote and nunchuk, but the amount of variety is commendable. Everyone can find a way to play the game and everyone can feel comfortable while doing it.