To do this, you will need to use Safari. I am on a Mac, so I don't know if this will work on a PC. But Safari runs on PCs, so give it a try. If this works for you on a PC, please let me know!
To download any YouTube video, open the page in Safari and then press command>option>A (I guess the command key on a PC is the Windows key, by the way). From there you will see a long list of files, go find the largest one and double-click on it. Safari will download the file, calling it videoplayback.flv. You can then rename the file name, and save it anywhere to watch at anytime. The file type, by the way, is Flash.
If you would like to watch it on your iPod, open the file in Quicktime, and do a save as, selecting as the format iPod or iPhone. That will save it as an mp4 file, which iTunes recognizes. Open iTunes and go to File> Add to Library. Then sync it to your iPod, and enjoy!