Let's see... this list is of ANIME? Not manga? Or both? If it's just anime:
1. Fullmetal Alchemist (jesus christ that show is amazing, don't let the manga fool you. It's very deep, it's very interesting, it's got many suprises, and everything is actually explained slowly (problem with some animes), and the action is very good at times). I was surprised to fall in love with this anime, but frankly, if it was a beautiful woman, i would make sweet sweet love to it. Hell, if it was a man i'd make sweet sweet love to it. Frankly, if i had it on DVD, i'd make sweet sweet love to it.
2. FLCL (Funny, weird, great. Some of hte best anime music ever).
3. Naruto (a great anime with an amazing ps2 game made after it. The actions amazing, the comedy is hilarious.).
Also 3. The kenshin preseries OVAs. They were just amazing.
4. Princess Mononoke (I thought that movie was amazing, what's wrong with you people?)
5. Trigun (it was just really good, waht can I say? Good action, good humor)
6. Inu Yasha (it's funny, it's actiony, it's just good.)
7. Vampire Hunter D: Bloodlust (a very nice improvement over the first animation wise and storyline wise. Just very cool in general).
8. Akira (It was a very good movie. Very interesting)
9. Neon Genesis Evangelion (This series was so deep if you through a rock down it, you'd never hear the splash. It was also very interesting, and overall well made, except..... many things just never got explained in the anime. That's why i'm reading the manga now. Also, the last two eps sucked, though the movie more or less made up for that.)
10. Hellsing (This series starts off GREAT. If i'd only seen the first 5 eps or so, i'd probably have put it 1st or 2nd, but sadly, i've seen more. Towards the end the series just decided to stop making any sense at all, and then promptly ended itself at episode 13.)
Now, as a side note, Cowboy bebop more or less deserves to be on that list just for it's music, but i dunno... i just didn't find the series as captivating as the other stuff on the list. Also, the Hellsing manga is just amazing, and probably ties in favorites with the Fullmetal Alchemist anime.
My girlfriend would probably put Kenshin and Wolf's Rain way up on the list.
Favorite anime music in general (can't give this any order frankly): Hellsing, Cowboy Bebop, FLCL.
Favorite songs specifically: Green Bird (cowboy bebop), Opening theme of Hellsing, practically any song from FLCL, and the 1st ending and beginning song of Fullmetal alchemst, as well as "Brothers" from fullmetal alchemist.