My boyfriend recently reformatted the computer and I forgot to back up my apps before he did so. I've plugged my phone into the computer for the first time, and realised that they're still on my phone, but not on the computer anywhere - so they don't come up in iTunes, and can't update any of the apps that have updates available.
Is there a way to get a copy of the apps back on the computer without having to re-purchase every single one?
Connect the iPhone and choose Transfer Purchases from the dialog box which appears or the File menu in iTunes. Do NOT sync the iPhone until you've completed this task.
On your computer, log into the same account that was used to originally purchase the apps in question, connect your phone, DO NOT SYNC, Store>Authorize this Computer, then File>Transfer Purchases. The iTunes content sync is one way: Computer to Phone. If this is a computer other than the one your phone was last synced to, ALL itunes content will be deleted from your phone when you first sync to this computer. If you transfer your content BEFORE you sync, you can select the same content to sync back to your phone.
If your iTunes library - the iTunes named folder located in the Music folder was included with your computer's backup, the apps would not be lost. All apps on your iPhone should be in your iTunes library on your computer and will be with Sync Apps selected under the Apps tab for your iPhone sync preferences with iTunes, which are stored in a Mobile Applications folder in the iTunes folder.
The computer needs to be re-authorized with your iTunes account with iTunes if you haven't already done so.
With your iPhone connected and without syncing, at the iTunes menu bar go to File and select Transfer Purchases From - the name of your iPhone.