I have the same problem.
I've tried every suggested fix I could find on the forums and google, and also a suggestion I got when visiting the Mac Store. Nothing solves the problem permanently, but I have found a quick fix to get applications to open:
1. Download a new application. It opens for a split-second and then closes.
2. In iPhones, deauthorize your computer, then reauthorize it.
3. Connect and sync your iPhone to iTunes.
4. Now, trying the application, it works!
HOWEVER, new applications I download have the same problem, and I have to repeat the method above to get them to open, EVERY TIME I download new applications. So, every time I want to use a new application, I need my laptop and a working internet connection. Very annoying!
Methods I've tried that have failed:
-Restoring my iPhone (I tried this today, and now have 3.0.1 running)
-Deleting applications and reinstalling them
-Rebooting the phone
-After downloading a new app, running other applications that work
-Making sure my iPhone and Macbook use the same account on iTunes
Anybody out there know a fix for this?