The guys on MacBreak Weekly back up what I've experienced: Installing apps via App Store on the iPhone just spells trouble. Do it only through iTunes.
UPDATE: This … umm … feels less true, and since iTunes 8, the process of downloading and updating apps is a lot better. But I’ve got a lot of hope placed in iPhone software 2.1, coming out tomorrow, as my 3rd-party apps just started crashing again, after a full 2 weeks of stability.