Is there a way to see all iPhone App Store purchases?

This is now possible since iOS 4.3.3 by going into the iPhone App Store > Updates > Purchased. It provides a list of your iPhone app purchases and allows redownloading from the iCloud.

Also you can visit reportaproblem.apple.com and all recent purchases will be shown.

I don't think there is a way to view just iPhone App purchases. You can view your whole iTunes purchase history. You can see your iPhone app purchases there.

Open iTunes -> Store menu -> View My Account -> Sign in -> Go to Purchase History

Update: This seem to include all your purchases using your Apple ID (iOS App Store, Mac App Store, and iTunes Store)

On iOS, go to Settings > [your name] > iTunes & App Store.