As I like a lot of anime, it's hard to pin down my favorites. Still, these are probably my more noteworthy finds (in no particular order):
Vision of Escaflowne (series): First series I actually bought. Mixes two things that appeal to me: fantasy, and mecha. One of few shows where I can't pick out a character I dislike.
X (series): Second series I'm in the progress of buying. Enjoyable music, nice artwork, high-powered action, and a looming crisis. Big inspiration for a game I hope to get off the ground sometime before our own world ends...
Read or Die (OAV and series): Haven't finished the series, but I've enjoyed what I've seen so far.
Cowboy Bebop: For reasons listed.
Trigun: Liked the characters and setting, though the ending was merely 'ok'.
Neon Genesis Evangelion: Tends to be a love it or hate it show. I rather like it, despite some problems towards the end.
Spirited Away: Not quite as good as I was hoping...but I still bought it. As I get fansubs for most shows, I really only purchase things I like a fair bit.
My Neighbor Totoro: A cute show with very little to dislike about it
Grave of the Fireflies: A rather stark contrast to the last two I listed...
There are also a few that I've only seen one or two episodes of, at conventions and such. GetBackers, Risky/Safety, Macross Zero, Gunslinger Girl, Hellsing, Gunparade March, and Boogiepop Phantom have all caught my eye. I'm sure I could dredge up more if I really wanted to.
Now if I could only find the time and money to watch all of this stuff
