I have the same problem. Rebooting doesn't work. Re-syncing doesn't work, either. It just started last night. Every downloadable app that didn't come pre-installed crashes while it's loading.
I downloaded updates to the Facebook and Bank of America applications. I don't know if it's related, but I thought I'd throw it out there in case anyone else did the same.
What firmware version do you have on the iPhone...most apps (especially updates to previous apps) require 2.2 minimum. While the AppStore on the iPhone fails to tell you this, if you look at the app via your computer/iTunes you can see the requirement. If you put lets say the new Facebook app on your iPhone and your iPhone is not 2.2, it will not work....but I sort of thought it would tell you but could be wrong.