Can I get the apps I bought from the app store back after my iPod touch was wiped?

To go into a little more detail.

I sync my iPod touch every now and again and the apps pop up in the list in iTunes but recently I bought a few small apps (like Peggle in the sale) and before I had a chance to sync someone plugged my ipod into another PC and chose the wipe option.

Does Apple remember what apps I bought so I have re-sync and get them back or do I have to buy them again?