Another anime fan here - mostly movies though. I've seen most of Miyazaki's movies and other Ghibli films. I've enjoyed Appleseed, Ghost in the Shell, NGE, Akira, Vampire D, etc. Others in my collection include Afro Samurai, Barefoot Gen, other manga films (5 centimetres per second, Origin, etc.) and the work of Mamoru Hosoda is beautiful and intelligent.
I massively love Cowboy Bebop and I have the whole series on a rare set of DVDs. Another film fave is Blood The Last Vampire - short but superb imho.
I'd like to get a few more anime series to watch but at the moment I'm still working my way through a bunch of other stuff!