MKDS. I guarantee you it's the best Mario Kart game to date.
You can also play against other people with the game, allowing each person to choose their racer/kart and giving a wider selection of tracks. But the main multiplayer experience if via Nintendo Wi-Fi Connection. You can play with anyone around the world and play on an agreed track.
I gave this game a Hard difficulty rating as some parts of the game can be very challenging, such as the higher engine classes of Grand Prix, but most importantly, completing all of the missions, especially with at least 1 star rating on each, which gives you stars next to your name on multiplayer corresponding to how well you did. I set the learning curve to high because anyone can pick up the game and have a blast, but to beat the really competitive veterans via Wi-Fi you need some skills, such as snaking and boosting around corners well.
I only have one thing else to say. If you have a DS, and you don't already own this game, get it, and you won't regret it.