Comedy- Melancholy of Suzumiya Haruhi (Watch the first episode last. Very witty comedy.)
- Sayonara Zetsubo Sensei (Morbid comedy)
- Yakitate!! Japan (Comedy about bread, and yes, it's good!)
- Ichigo Mashimaro (Cute girls doing cute things, best way I can describe it; funny.)<- imo better than Azumanga Daioh
- Great Teacher Onizuka (Ex-thug becomes a teacher)
- Welcome to the NHK (uh, yea, a hikikomori tries to integrate back into society)
Action - Black Lagoon Season 1&2 (A salary man turned mercenary)
- Samurai Champloo (If you liked Cowboy Bebop, this anime is for you)
- Gunslinger Girl (Government sponsored brainwashed assassin children)
- Utawarerumono (About a war between humanoids)
Mecha - Eureka Seven (boy meets girl. Very good character development and original mecha ideas)
- Heroic Age (War between races in space)
- Full Metal Panic Season 1&2 (ex-soldier boy works for merc group)
- Rahxephon (Not-quite-as-emo as Evangelion)
Drama - Monster (Wow.)
- Darker than Black (Eh, unique people with unique powers)
- Kimi Ga Nozomu Eien (Get the tissues)
- Paranoia Agent (Uh, yea, can't really explain this one)
- Shingetsutan Tsukihime (Vampire teams up with a guy who can see the lines of life)
- Elfen Lied (Going against my better judgement but it's still entertaining. Lots of blood. I mean it.)
Those should get you started. I think a couple are licensed, but I have everything here except Darker than Black on one of my HD, I just threw a bunch down which I give my seal of approval. I have more on my HD, just can't think of any that jumps to mind at the moment. I'll go check later what else I have that's good. All actions scenes are guaranteed to be cheap budget free. (no still action pics with a black screen with a flashy line to represent a sword strike/punch/magic power). And no retarded "I'M CHARGIN' MA LASOR! while you talk shit" for 4 fucking episodes (Naruto, DBZ). And the annoying bitches are kept to a minimum