I would go for Pure until Joyride comes out.
Pure isn't a cartoony racer and you can't do things like drop banana peels and throw shells at other racers but it is a fun ATV racer that lets you do tricks and earn boosts to use in races. It has online racers but last time I tried to play online there wasn't much activity but they are doing a bundle with that game now so the online on it might pick up.
You can download the Pure demo from Xbox Live here.
If boosting and car crashing carnage are what your looking for then Burnout Paradise is also a worthwhile look, again it's not got a cartoon style and doesn't have the power up style stuff of Mario Kart but it's a fun arcade style racer with some cool looking cars and an active online community. On top of that the developers have really supported it by adding tons of extra content for the game, some free and some paid for. There is a (paid for) downloadable content pack that allows you to buy cartoon looking cars.
You can download the Burnout Paradise Demo from Xbox Live here.
There are also a few Xbox Live Arcade games that might be what your looking for, I haven't played them but the descriptions sound like they maybe what you are after.
Xbox Live Marketplace for Racing has games like
GripShift and
Mad Tracks (both should have demos and allow you to buy the full game online). Both the games I mentioned have paid for expansion packs but the standard full games are 800MS points which I think is about £7 (but you buy points in packs so you'll probably have to pay more for more points).