Actually, I'm not really much of an anime fan considering I live in the SF Bay area. I know next to nothing compared to most people I know.
Code Geass is arguably the best anime series in the last few years and is available online in it's entirety (2 seasons)
here.
Ghost in the Shell is my personal favorite series (and two great films, of course). I'm not sure if it's available streaming online, but I suspect it is somewhere.
Neon Genesis Evangelion is widely considered to be the most successful anime series of all time, though the last few episodes are really quite confusing. The series is also online,
here.