Koelling: not to worry, because the authorization somehow knows your computer. I believe it's probably based upon the MAC address, which is unique to every computer. It doesn't matter if you forget to unauthorize a computer before you reformat and reinstall because the server knows it's still the same computer.
I ran into this problem and spoke extensively with a tech at Apple about this. My OS X installation got hosed, and there was no way I could access iTunes to deauthorize before I reformatted and reinstalled... so I sent an email to the nice folks at .mac requesting a deauthorization of that installation, and they replied that it wasn't necessary -- that when I reauthorized the songs after the reinstallation that it would still be the only authorized computer. They wouldn't explain exactly how they knew it was the same computer, probably because they didn't want to share their authorization system with just anyone, but I was assured that I could reformat and reinstall to my heart's content and it would still be only one authorization.
I have now reformatted and reinstalled four times (for various reasons) and authorized my purchased music five times now, all on one computer. Each time the authorization has gone through just fine. Trust me, the server knows your computer and doesn't care if you reformat and reinstall. People have speculated that there's some hidden file stored on your computer keeping track of authorizations, but there's not... it's all server-side stuff, and it's damn smart, too.
So, cf25, your logic just doesn't hold, although I thought of the same thing when I first started purchasing music from the iTMS. Each computer that you copy the file to must be authorized through the internet through iTunes in order to play the file. The authorization does NOTHING to the files themselves. So even if you've only authorized one computer to play a certain file, then you copy that file to 5 other computers, only two other computers will be able to play the file, since you have to authorize through the internet before you can play it. If you try to play it on the fourth computer, then when iTunes asks you to authorize, you'll be rejected... until you unauthorize one of the other 3 computers.
What I'd be interested to see is if new, third-party media players like iTunes that don't use Apple's authorization scheme and CAN play MP4/AAC files will play an iTMS-bought AAC file, or whether you're stuck using iTunes to play the music you purchased through iTunes. QuickTime plays my purchased music just fine, but I haven't had the opportunity to try and play a purchased AAC file with QuickTime without having authorized through iTMS first... that would be interesting.