As @Vaishakh said, there are games for App Inventor, including Mole Mash (which I wrote). I've also written a game in which you can move a sprite by tilting the phone, having it chase or avoid other sprites.
@stonemetal was right on about the pitfalls and limitations. At least for now, there's no way of extending App Inventor, so if you want to do something not built in to the system, such as 3D graphics, you are totally out of luck. There are also limits on the language, such as the inability to pass a component as a parameter or to have local variables, which provide a practical, if not theoretical, limit on the size of a program. The App Inventor implementation is also not optimized for high-performance games.
I'd recommend App Inventor as a way to help someone new to computing or intimidated by the SDK to get started with creating games. It can also be good for creating mock-ups or prototypes. Some games (such as quizzes) can be implemented just fine in App Inventor, but I'd recommend the Java SDK if you want to build a complex game with lots of objects and high performance. The App Inventor team (which I'm part of) has just released a library to help ease the transition from App Inventor to the Java SDK [http://groups.google.com/group/app-inventor-instructors/browse_thread/thread/10a64e64b7886afb].