Sailor Moon(original Japanese version) has some awesome music. FLCL and Cowboy Bebop are two of the best anime soundtracks ever, I would have to agree. InuYasha has some awesome background music with a very old time traditional Japanese feel, and the intro and ending songs are awesome as well. My favorite would have to be Grip! by Every Little Thing, which is the 4th intro song. Sango's Theme is my favorite background piece. I also love the intro songs to Sayuki, Super Gals, , Outlaw Star, and Sakura Wars. And the most beautiful ending song ever would have to be Melfina's Song from Outlaw Star(next to Yoko Kanno's Blue anyway...
Yes, I am an otaku...sue me.