Keep in mind that even though I have these numbered 1 through 10, the order I put them in means almost nothing, they are all great series and what I may consider my favorite may depend on my mood at any moment.\
1.Cowboy Bebop - The scene in which Spike first confronts Vicious at the church remains one of my favorite anime scene of all time due in no small part to the music.
2.Wolf's Rain - Not quite sure how to explain why I like this. I could say how it has such great music and characters, but that all just sounds rather generic and doesn't do the series justice.
3.Fist of the North Star - Kenshiro, nuff said.
4.Yu Yu Hakusho -For me this show is a classic and one of the shows that got me interested in anime. It may sound like I'm just being nostalgic, but I think that Yu Yu Hakusho is the show that Bleach is trying to be.
5.Beck: Mongolian Chopsquad - Very identifiable characters and freaking great music
6.Code Geass - I first watched Code Geass after I got tired of listening to my friends pestering me about it. I was not Dissapoint.
7.Full Metal Alchemist: Brotherhood - This series gets major points from me for following the Manga Storyline as opposed to the original Anime.
8.Sgt. Frog - I don't watch too many strictly comedy based anime, but Sgt. Frog is freaking hilarious.
9.Deathnote - Really like the mind game aspect of the series and the whole "absolute power corrupts absolutely" thing where it could almost be said that Yagami Light and Kira are two different people.
10.Gurren Lagann - I was originally a bit hesitant to put this on the list (I guess I somehow had to choose between Code Geass and Gurren Lagann being on the list) but in the end I had to give in because of those epic moments which are just so satisfying to watch.
Berserk: Good show, but I can't put it on the list because of how badly they botched the ending. If this were a top 10 manga list, berserk would take #1 for me. The anime is certainty worth watching, just be aware that you will have to read the manga if you want the ending to make any sense.
Neon Genesis Evangelion - For me EVA is a good series with the only things holding it back from being great are the ending and some issues I have with Shinji's character development