List of all apps bought from App Store?

Do you sync your phone often. Each time you sync a copy gets put on your computer in iTunes for backup (which is why you should be syncing often).

Even if you uninstall from the phone, the copy is still there in your application list in iTunes.

Do you still have old computer. All the files are on there. You just need to bring them over.

Well I don't have iTunes here at work, but there is a place somewhere when looking at your account to look at past purchases. Just forget how to get there.

Also if other computer is around, you can at least look at the folder it saves the apps to and see all the files for each app and get a listing that way.

Do you keep a copy of the receipts that itunes send you through e-mail? I kept all of my e-mails from Itunes in a separate folder so I know what I downloaded (free or paid).

try this ... from your computer, in ITunes, go to iTunes Store
QUICK LINKS > Account > Purchase History