AMV
AMV stands for "Anime music video", a very popular pastime amongst anime fans. The general idea is to take a song that is familiar to your friends and then find a bunch of anime clips that support the lyrics (lip-syncing the words). If you do a search on the initials "AMV" on YouTube you'll pull up a result of MILLIONS, however many of them are quite mundane, simply showing scenes from a popular anime program while playing a familiar song. But the more creative ones actually try to add something to enhance the viewer experience in some way, such as having the clips follow a specific theme, transitioning the figures in and out, and of course having the characters "sing" words appropriate to their programs and specific backstories.
The wikipedia has an article on trend here:
http://en.wikipedia.org/wiki/Anime_music_video
Here's an example that shows how creative they can be. The music is "Spirit Never Dies" by power metal band Masterplan. The clips appear to be from Naruto, Cowboy Bebop, Bleach, and others I don't recognize.