Is it all your apps or just downloaded ones? Does calculator run OK?
If it's just the downloaded ones it's quite a common error, and there are several suggested fixes:
- de-authorise and re-authorise your iTunes account
- download a free app from the app store
- delete all the apps from the phone and redownload them
- delete all the apps from iTunes, sync and don't transfer the apps back, redownload the apps in iTunes and re-sync