If you have to problem that some apps crash directly after running them, i.e. you see the app “popup” but it immediately disappears leaving you back at the home screen, it might be a problem with Apple’s DRM. This can occur if a Sync with iTunes is aborted or the connection was lost.

I found the solution between the comments on iphonehacks.com: Just download any (free) app from the AppStore - might also be some app you already bought but deleted from the phone. After the app is installed, all other apps should work fine again.