I watch with subtitles only - no dubs. Huge series (Bleach, Naruto, OnePiece in Japanese ONLY) have too much filler to be great IMO. I'm not even going to mention them.
1. Rurouni Kenshin
2. Higurashi no Naku Koro Ni ( This one rules so hard - warning - lots of blood, murdering, violence, torture, and criminal insanity. If you watched Elfen Lied - you might like this too.

The below video clip got me interested, I watched the whole thing AND a spin off [ worry not, no real violence in the video - except Rena getting pushed. ] )
3. Samurai Champloo
4. Cowboy Bebop
5. Hellsing
6. Gantz
[ame="http://www.youtube.com/watch?v=c1R6jK52tS0"]Rena from Higurashi being crazy[/ame]
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If you like the Anime, try the Manga. It's always better.
[ Other series I find notable: Full Metal Panic, Pumpkin Scissors, Kiddy Grade, Najica, Abenobashi, Galaxy Angel, Chobits ]
If you find your self getting into manga - try this series:
Black God
Seriously. It rules hardcore.