Looking up Already Purchased iPhone/iPad Software on iTunes

On the desktop version of iTunes, go to the store. Click on your account name on the upper right hand corner of the store pane, and then click on Purchase History.

iPad user manual, page 95:

"To see all of your purchases, sign in to your account, choose Store > View My Account, then click Purchase History"

edit: beat me to it!

This is how i got my apps back after my first iPod touch died. I didn't have em backed up. I do now!

The problem is, if you're like me, and download lots of free apps, they all get added into your purchase history. Then when you look at it, it's a mile long and you have no idea which ones are good / bad.

If they would let me download the entire thing in one shot as a CSV file, I could maintain it on my own.

If they could update iTunes so that if you did NOT purchase something, it asks you before purchasing it, "yes or no". Happened to me yesterday, an app I thought I purchased, I clicked on "download" because I was trying to synchronize two different machines (both authenticate) and I ended up purchasing an app that I didn't want to. If you already purchased it, it prompts "Do you want to download this again?" but no confirm buy if you do not own it already.