I stopped watching a few years ago but have watched a ton in the past -- what are you into? You should look up anime flowcharts to see what you should watch based on your interests.
All-time favorite series: Neon Genesis Evangelion, Escaflowne, Saishuu Heiki Kanojo, Serial Experiments: Lain, Prince of Tennis, Love Hina, Samurai Champloo, Cowboy Bebop, Chobits, Death Note, Naruto, Bleach, School Rumble
All-time live action: Great Teacher Onizuka, H2
All-time favorite movies: Akira, Ninja Scroll, Escaflowne Movie, Tenchi Muyo! movies, Mononoke Hime, Spirited Away
WTF did I just watch: Mouse, Gravitation, Raimuiro Senkitan
These are all over the place... for a new watcher I'd recommend Cowboy Bebop or Samurai Champloo, they're from (played on not made for) Adult Swim so they're a little more American-ized, or at least more widely accepted/available. School Rumble is hilarious, most people would like that too if you find good subtitles.