I could go on for ages on this topic.
Most of my favorites are really obscure. The best, most deep and artistic anime ever on the planet is Haibane Renmei. That is no doubt my favorite anime ever. If you haven't seen it, you should. It's really short, only 13 episodes long, but it's seriously AMAZING!
Now that I've beat that horse to death, Kaleido Star is a really cute series. And, of course, the anime that started the obsession for me was Rurouni Kenshin, which is still one of the best of seen (Just Rurouni Kenshin. No Samurai X. Ever.). Of more recent anime, I highly enjoy Code Geas, although I haven't seen much yet, and Bleach is okay. Death Note is also good.
Tsubasa is one of my favorite series ever, except I hate the anime. I love the manga to death, it is so beautiful and brilliant and the best thing Clamp has ever done. I think the anime dumbs the story down way too much and the art is so much worse.
^No1 fan. Hurray for minor characters!
Sometimes I get the urge to conquer large parts of Europe.
Butler loves the Carebears, especially Funshine bear.