So my iPod had been "broken" for a few months and I just figured out what the problem was. You'll never guess: Microsoft Windows! Apparently, Service Pack 2 (SP2) has problems with updating the Windows Registry and this can cause any Plug and Play devices to fail (bug KB893249). In my case, it seemed like whenever I plugged in my iPod, the computer would recognize and then immediately unrecognize the device over and over again, in a loop. It would sometimes work and then fail, sometimes tell me to update my iPod and all other sorts of crazy things.

Anyway, to fix the problem, you basically need to go into the Registry and delete all records that contain "iPod" and then reinstall the iPod software. Here are all related links that I found that solved the problem. You'll see the Apple and Microsoft sites are extremely UNHELPFUL, but the friendly users at annoyances.org have the answer.

http://docs.info.apple.com/article.html?artnum=302898
http://support.microsoft.com/default.aspx?scid=kb;en-us;893249
http://www.experts-exchange.com/Operating_Systems/Q_21641885.html
http://www.annoyances.org/exec/forum/winxp/1132874240
http://www.annoyances.org/exec/forum/winxp/t1051715405