I'm most into the emotionaly intense and "I'm trying to do the right thing" type so I like best:
Kenshin Yeah!! rpgchocobo it is really something. and the OVAs too. I'm amazed that so many people don't get(as in understand) this series, the dialogs are so deep and brilliant, and the relations between characters so developped.
Trigun it gets deaper and better to the very end. And I though at first "look at that, another absurdly funny anime"(nothing wrong with that) I was soooo wrong, this series has it all humour and drama to the max
Naruto a little on the light side but more intense then most
All the above, call me emotional, brought tears to my eyes.  
 
 
Goldenboy this one surprised me also. I though at first it would be like Love Hina or something but it manages to be very deep with a great sense of honor and a will to do the right thing, while being very funny and sexualy oriented.
Less in the genre but great:
Cowboy Bebop a graphicaly and musicaly masterpiece. I found that the plot let you down a little near the end but still a joyride for the most part.
Like also:
Wolf's Rain
Hellsing (mostly because there are undeads and you gotta like undeads)
.Hack (mostly because I dream everyday I could live in a fantasy RPG  

 )