AMVs, or Animation(Anime)MusicVideos started out as a cult back in 1982, and the very first AMV was created using a very violent clip from the anime Space Battleship Yamato mixed with the Beetle's song "All You Need is Love".

There are 3 types of AMVs/MAD (MusicArtDance)

Beat sync - AMVs that sync the motion of the music to the these make up a majority of AMVs

Lyrical sync - They pick clips from one or more shows and sync them to the lyric of their song of choice

Mood sync - Using effects the editors of these types of AMVs will manipulate the mood of a series of scenes to fit the mood of the song

In the end it's always about motion, and music. Whether it's motion of emotions, motion of lyrics,

Here are a few AMVs that are great examples of the various types.

Spirit Rush - Mood Lyric, and Beat Sync

http://youtu.be/-Maokq-4rp8

Keep Your Eyes Open - Lyric, Beat, and Mood Sync

http://youtu.be/KAAoLAcZTAA

Teenagerrrrs!! - Beat, and Lyric Sync

http://youtu.be/0LarHK5NSMM

I'm so Classy - Beat and Mood Sync

http://youtu.be/NbonMpSXBEI

Programs that are often used include After Effects, Sony Vegas, Premier Pro Photoshop, Illustrator, and Final Cut Pro X.