Due to all the accelerometers and sensors that every company likes to put in their gadget nowadays, there's been a new market for racing games. You can easily use a tablet as some sort of makeshift wheel to control your car, and even if you don't have pedals or a stick-shift, you can still make do in a racing game. Note that there's a lot of games on the Android and this list is nowhere near exhaustive. With this disclaimer, here goes:
Alright, it's not really a racing game, it's a racing team management game, but I couldn't help but put it in the list because of the well drawn cartoony graphics, in-depth gameplay and huge charm. It counts, dammit. There's a lot to the game too - although you don't control the races themselves, basically just being a "set your baby in the wild" scenario where your driver and your car do what they can to win you some money, you will still hold on to every pixel your driver gains against and your opponents. You'll want to succeed, you'll want to upgrade and participate again and again.
I'm still in awe of the fact that these guys can actually put out a game almost every month. Granted most of Kairosoft's games are basically re-skins with different stuff in them, but having such a small turnover on development is certainly impressive.
The seventh in Gameloft's series of Need For Speed inspired racing games, Asphalt 7 seems to have nailed it more than the others because of the fast and enjoyable driving style, giving you more to satisfy your need for speed even than the eponymous titles. It doesn't look as great as the game lower on the list, nor does it have as much depth to it, but it's an enjoyable game that you can buy for 7 times cheaper. You take what you can get.
You generally don't expect great graphics from mobile games, but NFS Most Wanted certainly delivers, bringing almost current-gen console graphics to portable devices. There's car damage, online play, police chases, customizable cars, a huge amount of storage needed. It also starts warming your device up a bit, but that depends on what device you have. It's fast, it's furious, it's not Fast and Furious, it's Need For Speed, and it may be its best entry on the market right now.
Again not really a traditional racing game, Earn to Die is what I think is the essential portable game - it can be played in bite-sized brain chunks, it has a persistent upgrade system, it's satisfying, it has zombies, and you can turn a small banger into a zombie killing machine. It's fun, it's got explosions and monster trucks, it's got a ton of upgrades, 8 kinds of vehicles, ragdoll zombie physics... what more can you ask for? And for less than the price of a coffee, it's great value as well. Get it.
This game is something else. It evokes feelings of Ignition and Death Rally in my brain, which makes me giddy. It looks great and inviting, there's fully upgradeable cars (even a School Bus!), a career mode, multiplayer and of course, nitro boosts. It's fun, it's frantic, it's quite great. It's even got Editor's Choice from Google, that's gotta mean something.