Youtube Archival
Saving Youtube videos is one of the easier things to do. (Storing them is not as simple, but that's a topic for another day.)
Youtube-dl is a cross-platform python script that easily downloads videos from Youtube, Vimeo, Google Video, and most other download sites. Better yet, you can even put videos in a playlist, and it will download them all.
Get it here:
First, get the script. Then, make a folder to put your videos in (C:\Videos for Windows, ~/Videos for Linux). Once that's done, run this command:
Windows
youtube-dl.exe -twc http://youtube.com/<video or playlist to download>
Linux
cd ~/Videos # Or wherever else you want to put the vids
youtube-dl -twc http://youtube.com/<video or playlist to download>
You can set a few extra options for youtube-dl. Most of them are not