There are a couple of programs that save YouTube videos, such as Video Grabber and ClipGrab. The programs are both free to download and can be used for more than just YouTube. Both work on Vimeo, Dailymotion and Yahoo! video.
ClipGrab allows files to be converted or kept in the original format. ClipGrab plays MP3, MP4, OGG Theora and WMV formats. ClipgGrab also has the ability to convert video files into MP3 audio-only files.