The Offending Screen (arstechnica)
The unlocking info from Apple is impractical for people who don't use iTunes or no longer have an "authorized" computer with iTunes (the whole stupid "authorization" thing as well as the bad interface of iTunes means that my iPod has never known its embrace - I use an alternate file management software for my 'Pod that gives me more freedom). Opportunistic developer MaxSoft even sells an "iPod unlocker" for $10 that essentially duplicates the easy hack you can implement from any computer that'll unlock your iPod in less than a minute. As always, there's the slightest chance you could screw something up when you crawl into your iPod's actual data, but this is worlds better than reformatting your iPod's brain and losing everything.
The easy fix (as outlined on a few of smarter websites that don't just reiterate Apple's dumb statements):
1) Open your iPod as a flash drive (you'll see it from the "My Computer").
2) Enable hidden folders and go into the folder "iPod control".
3) From within the "Device" folder, find the file titled "_locked" and rename it to "_unlocked".
Then just disconnect the thing and you should be on your way. If this doesn't work (I haven't tested this on any other iPods), deleting the file instead should work, but I would suggest that you Google around before you try anything other than this easily-reversible method. I've given you more than enough search terms should you need to look.