How can I delete a paused application download on my iPhone?

Solution 1:

If you can't delete the paused download (which, I'm thinking, suggests you aren't on the most recent release of iOS), then the simplest option that doesn't require a restore is going to be to find a WiFi hotspot and let the app finish downloading. Personally, I'd go that route (especially if out-and-about or on vacation, etc.) before wiping my data and having to restore again.

Alternatively, leave it on paused until you get home to your primary network. Your phone doesn't care two cents about your paused app downloads, so it shouldn't get in the way of anything.

Solution 2:

I can confirm that paused downloads get removed by rebooting in iOS 5.