The problem: All of the App Store app's on iPhone stopped working. You tap any App Store app's icon on the home screen, the app's splash screen appears, and a few seconds later the home screen reappears. Bah! Life without iBowl! You are ruined!
Half a fix: Install, update, or remove any App Store app. The App Store asks you to log in again. After you type your password and the App Store manager takes care of its business, everything is back to normal.
The cause: If you haven't associated your PC's iTunes installation with your iTunes account, then whenever you sync your iPhone with iTunes, your iTunes deauthorizes your App Store app's. This can happen if you have never made the association, and it also seems to happen if you reinstall or upgrade iTunes on your PC.
The fix: Run iTunes on your PC. Click Store / Authorize Computer. Sync your iPhone with iTunes, and everything is good again.
Thanks to Ken Loh for the clue.