Another - Its not horror in a scary way, but it has a nice mystery. The series does use alot of gore; episode 8 was a shocker.
Akira - You can't go wrong with a classic. Either the manga or anime is just fine, but I would go with the manga.
Death Note - While interesting at first, the show loses steam after episode 25 or 26. The show is about a guy who finds a note book that can be used to give people heart attacks and he uses this notebook to kill criminals.
Elfen Lied - I haven't watched this series to the end, but many say that it is really good. The first episode is full of nudity and even more gore. There is a point where the main character uses a headless secretary to shield herself from a barrage of bullets.