I was having a lot of trouble on how to transfer apps from iTunes to iPhone.
I tried doing backups and full syncs to no avail. Finally, in a moment of desperation, I righted clicked on my iPhone and chose the option “Transfer Purchases” and to my suprise and glee I successfully moved my applications onto to my computer.
To transfer applictions to iTunes from your iPhone:
Right click on your iPhone in the left hand explorer bar.
Select “Transfer Purchases”.
You should see a progress bar in iTunes and your phone should read “Sync in Progress”,everything went as planned, all of your applications that were purchased on your iPhone should now appear in iTunes. iPhone Transfer can also help you solved this problem.