For games,
Robo Defense is a fantastic tower defense game which has a free version, and your progress carries over if you decide to upgrade. You earn points for every game you play, whether you finish it or not, and you can spend them to unlock new towers, increase starting money, improve permanent upgrades, etc.
If you like RPG's, the Zenonia series is pretty good as far as graphics, storyline and dialogue. It's kinda like a JRPG, it has those anime-looking characters, and has three different classes to choose from. There is a quest system and skill tree available as well as basic stats that you can bank when you level up. Combat is open world, just walk up to enemies and start attacking. Zenonia 1 and 2 cost $0.99 I believe, while 3 may still be free.
Pocket Legends is a fun little MMO, you can choose from three classes and take quests with other players online. The UI could use a little work, as far as finding the map and figuring out a good way to manage your inventory, and it updates all the time. It's still pretty fun and the controls really work well, and its free to play.
SpeedX 3D is an addicting race survival game that uses the accelerometer in your phone to steer your first person view out of the way of walls, holes, and other dangers on a dynamically changing course. It has several speeds which can get insane, and includes a challenge mode which resembles a story mode that eases you into all the hazards of the game. Free as well.
GameDevStory is my absolute favorite game for the Android. Its a little sim where you own your own game development studio, and you're in charge of everything from naming the games to hiring the people. You go to press releases to learn about new consoles from companies like "Intendro" and "Senga", and then can buy licenses to develop games on that new platform. You can gain a fan base, attend yearly electronic shows, and even win awards at the end of the year for your games. There is a free version, but it only lets you play for I believe two in-game years, and though it says you can port your progress over I never got it to work for mine.
Other than that (all of which are free),
Mangler
PC Monitor
ReadIt (Gawker Media News Articles)
TIKL
Revision3