I jailbroke my phone and have apps for free, usually when I sync it, only the apps that Ive downloaded through my computer will remain on the phone.
All the others get deleted.
When the iphone connects to the itune, click the right-hand mouse on the name of your iphone (on the left column, it usually appears when Iphone gets connected) then select transfer apps, it will transfer your new apps to your computer. GL!