Dual! Parallel Trouble Adventure (14 ep)- Great series, kind of light hearted.
Saber Marionette J (26ep - 6ep OVA - 26ep)- All the series are pretty funny, and got some decent drama thrown in.
Silent Mobious (26ep)- Interesting series
Outlaw Star (26ep)- Fairly standard, but still good
Neon Genesis Evangelion (26ep)- Just watch it
Hellsing (13ep still ongoing)- Future-Goth vampire series
Naruto (46ep Still on going)- Another preety good series
Cowboy Bebop ( 26 eps + 1 movie )- easily the most artistic anime ever produced. space based bounty hunter anime with awesome character development, and some great fight scenes.
Neon Genesis: Evangelion ( 26 eps + 1 movie )- make sure you hide the rope before you watch it. 3 kids pilot Evas in an attempt to save the earth from angels.
Bubblegum Crisis: Tokyo 2040 ( 26 eps )- hot chicks + hard suits + cyberpunk = awesome. 4 girls take down the evil Genom corporation.
Serial Experiments: Lain ( 13 eps ) - a different brand of cyberpunk. realities blend as lain becomes god of a new reality... or something like that.
Furi Kuri ( 6 eps ) - A kid who sprouts robots out of his head and a girl from another planet battle bigger robots with guitars. weird, but great.
Love Hina ( 25 eps + 2 movies ) - 3rd year ronin Keitaro takes over his grandmother's all-girl dorm. lots of laughs and fan service.
Great Teacher Onizuka ( 40 or so eps ) - Former gang member Eccichi Onizuka persues his dream of becomming the greatest teacher in Japan.
Robotech ( 36 ep Macross saga ) - One of the first successful animes in America. Robots galore, and a romantic storyline.
Gundam Wing ( 50 eps ) - another giant-robot anime. well animated, and with great characters. An epic plot revolving around control of space.
Mahoromatic ( 12 eps ) - A female battle-robot is allowed to live out her remaining year as a maid. Pretty funny, with some nice action.
Full Metal Panic ( 24 eps ) - Mech pilot assigned to protect Chidori by blending into high school setting. Lots of action, and some great comedy.
Initial D ( 39 eps + 1 movie ) - Tofu delivery boy Takumi becomes the greatest street racer in Japan. Not a lot of depth, but it's a fun show.
Ghost In The Shell: Standalone Complex ( 10 or so eps ) - Cyberpunk done right with incredible animation and a decent storyline.
Tenchi Muyo ( 13 eps ) - A classic romance comedy. Tenchi lives with 6 girls from space who are all in love with him.
A.D. Police ( 12 eps ) - Sidestory to Bubblegum Crisis. Great cyberpunk cop drama, just don't go in expecting Knight Sabers.
Yu Yu Hakusho ( a lot of eps ) - Dragonball Z done right, with a quick moving storyline, more substantial characters and a darker story.
I know this is blaphemy to some of you on the same level that spitting on a cross might be, but I really didn't like Trigun or Rurouni Kenshin. I can't really can't give a strong argument as to why, so I won't bother trying. I watched the first few episodes of each in Japanese and caught a few in English, but they just never seemed to reach out and grab me.
I just used to watch all the Manga anime. I was never a big fan of the distinctly Japanese stuff, you know, the inexplicable storylines and unitelligable events. I own Guyver, Genocyber, 3x3 Eyes and stuff like that.