I'm a fan of many anime series. But I'll just post the few that I'm crazy about.
Saiyuki - Love it. A lot. :D I could ramble about it all day long if I want to. XD But I won't. It's very deep at some times and very amusing at others. I <3 Goku also.
Azumanga Daioh - A very silly and random anime. Has cutesy stuff in it too (cats, penguins, etc). It puts a smile on my face. ^^
Get Backers - A recent one I got into. I've only seen a few episodes, but I love it. Can't wait to get my hands on the manga (even though the arts a little different and such). The messages are somewhat hard to get, but I'll live.
Kaleido Star - It's a nice anime having the "aim for your dreams" theme. It's amazing to see the characters doing jumps and flips that I could probably never do. @_@
I also like other animes mentioned here, like Chobits, Angelic Layer, Rurouni Kenshin, and some others.