Do all games and apps designed for the original ipad work on the ipad 2?

Or do I need to look for games and apps that explicitly state they are compatible with ipad 2?

They all work, the ipad 2 only has added functionality (cameras etc) compared to the ipad 1 not any restrictions, however there will be apps that only work on ipad 2 at some point I would expect.

All iPad apps should work on the iPad 2 and most iPhone apps will work on it as well. This is handy because the iPad 2's cameras give it access to augmented reality apps, so you can play Star Wars Falcon Gunner on your iPad 2.

I wouldn't expect too many apps to go iPad 2-only, though. Really, only augmented reality and camera apps.