From a post over at Dannychoo:
What are your favorite anime theme songs?
I love the Ghost in the Shell songs. They make up some of my favorite openings out of all the anime I've seen (I love me some Yoko Kano).
http://youtube.com/watch?v=BYbxCygS-PU (SAC's Inner Universe)
http://youtube.com/watch?v=u8a-YSRv0ro (2nd gig, Rise)
Still going crazy over Still Doll, the closing theme for Vampire Knight. Wakeshima is just so adorable, and I love her voice:
Really love the Nodame Cantabile opening and closing pieces. Can't wait for the second season.
http://youtube.com/watch?v=0a-HV2wpeBw (OP, Allegro Cantabile)
Blood + also has some fantastic songs.
Inori - Lena Park's opening for the Romeo X Juliet anime probably makes for one of my favorite openings of all time. I get chills every time I watch it, and just that opening can sometimes bring me to tears (can't wait for FUNimation to make it available in the spring so I can finally buy it) :
http://www.youtube.com/watch?v=VY7iXJyy1ys (anime opening)
http://www.youtube.com/watch?v=Px2n_LrTG_8 (Lena singing the song in English)
Tank! from Cowboy Bebop of course
This brilliant song, The Garden of Everything, from the Rahxephon movie (you can't go wrong with Yoko Kano AND Maaya Sakamoto):
Well...pretty much anything Yoko Kano's touched, honestly. And all the FLCL songs.
http://youtube.com/watch?v=GfsV6oZyFds (FLCL ending, The Pillows' Ride on Shooting Star)
Cruel Angel Thesis from Evangelion of course....
Duvet from Serial Experiments Lain:
Opening and Ending for Gunslinger Girl:
http://youtube.com/watch?v=xEMjq9VpBSE (Light Before We Land)
http://youtube.com/watch?v=p9JgMHDEKWE (dopo il sogno)
That's all I can think of right now, but that's plenty. :)
It's pretty much the only kind of music I listen to these days (along with show tunes). I don't understand anything they're saying, but I love the music and the way the language sounds.