Actually, that works with free apps, but if, say, your hard drive dies (thanks a bunch for
that, Seagate!

) and you had items on it that you purchased from iTunes, you will need to re-purchase them in order to have them on the new computer. If you have an iPod that is accessible as a hard drive (e.g. iPod Classic, older nanos, etc.) that happened to have had the purchased items synched to it at that time, you can transfer the purchases off of the device onto your new PC, but it takes a bit of work. And if you have an iPod that's not accessible as a hard drive (newer iPod Touches, iPhones), you'll need to purchase software to access the files and download them back to the PC. If you didn't have a purchased item synched to the iPod at the time the PC's hard drive died, you're SOL unless you re-purchase the item through iTunes.
Unfortunately, I learned that the hard way in August when I lost probably $200+ worth of movies, TV episodes, etc., (not to mention a couple hundred GB of photos I'd shot myself that are completely irreplaceable) when my stupid hunk of $#@#@#&**$#$#@#$ 1.5 TB Seagate external hard drive opted to cease functioning. Not that I'm still bitter about that or anything.
/hijack