I don't watch much Anime anymore, but my fav music is off my favorite Anime's soundtracks.

Neon Genesis Evangelion, Inital D, Cowboy Bebop, The vision of Escaflowne, Macross Plus. The last three were done by the same composer Yoko Kanno. She's second only to John Williams in my book. She can do pop, techno, jazz, and classical orchestral. Watch Escaflowne and then Cowboy Bebop to see how different her music is.

My most listened to until I started listening to only podcasts was the music from Initial D. It's a racing anime and the music is called "eurobeats", and is perfect fast driving music. Do a youtube search and you'll find pretty much everything, I don't want to add links cause this would easily make this post 10 feet long just with Kanno's work.

EDIT: Also I don't watch Top Gear much since it became so obvious, but the first 6 seasons or so, have some of the best music uses. It's on Netflix instant, but I don't know if all the music is the same from when it was originally broadcast, but it's close enough to the original. Great uses of Craig Armstrong, who's also done some great work.

One band that never disappoints me is "Yo La Tengo". I love the shit out of them.