my guess is that your talking about daft punks's "harder, better, faster, stronger"
AMV means anime music video
Britney Spears - Circus (:
Evanescence-Wake me up inside
Doctor Pressure!
There is no Nightcore anime. Nightcore is a DJ and a remix style of music. People just tend to use anime pictures in fan-made music videos.
Shigatsu kimi wa uso and Nodame Cantabile are among the most popular romance and music anime.
music
You can download free anime mp3 music or anime at Limewire. To Download, just go to Limewire.com.
Animekeys
If you are talking about anime techno music, than there are many in Japan. Hatsune Miku is a very well known one in japan.
Some music-related anime: Mermaid Melody, Chance Pop session, and Lovely Idol.
Ichigo's sheet music database houses some the most popular anime sheet music for almost all of the common instruments.