I had this problem too- I went into application download overdrive, trying out a few paid apps and lots of free apps- very few of the downloaded apps would work- just show the splash screen and crash.
I removed the free apps from itunes, resync'd and it started working. Other people have had luck re-authorizing their computer
Hope this helps,
Simon
http://discussions.apple.com/thread....535&tstart=510
http://discussions.apple.com/thread....878&tstart=480