The most violent anime...
I watched quite a few of those.
The top 5 are definitely (not sorted):
Afro Samurai - over-the-top fighting scenes, quite fun actually to watch
Hellsing Ultimate - even more over the top

- Ultimate senseless gore and fighting sequences with people being literally ripped to shreds.
Gantz - once again people get killed here in many various ways. Unfortunately ending is very poorly done, the anime doesn't compare at all to the first part of the manga... (at some point manga also had gone bad)
Deadman Wonderland. People dissolving in acid - enough said.
Shigurui - A anime about a samurai school. One of the most violent pieces I've ever seen (like brain coming out of cut in a half skull). A lot of physical violence, sometimes very hard to watch. I don't recommend it though, the end is way too abrupt (like a book with missing half of pages) - most likely they were hoping to end the story in second season that never appeared... well, you can always read the manga though.
Others, that can be also counted as quite violent:
Elfen Lied - it more about psychological drama than actual violence... end the scenes are done rather poorly, if animation was better it would definitely had much bigger impact
Berserk - not really violent, until the last episode - I know that a lot of people will disagree here but I consider most of the scenes as quite normal among the mature seinens
Basilisk - great fighting scenes and a sad ending. Basically two ninja clans fight against each other to decide which kid will become the next shogun at the present shogun order. I quite liked it, but the plot wasn't too ambitious.
Zetman - not really a good anime, but its fun to watch sometimes. A monster fighting other monsters for justice. Quite confusing at some parts.
Jin-Roh the Wolf Brigade - its a anime movie, but its very realistic. An Alternate history type anime about militia.
Ga-Rei Zero - about an anti-demon squad. Overall quite good, but the ending of first episode might leave you very confused.
Shiki - it had only a few violent scenes (spoiler: like the doctor slicing up his newly undead wife to find a way to kill vampires). Its more focused on drama and existential questions than on violence itself
Jormungand - an anime about a weapon merchant and her bodyguards. Its more a comedy type anime, but it still can get pretty serious

The ending sound cue - "She is loco" - describes it very well

Texhnolyze - very dark anime but also quite strange... main character finally decided to speak at the end of the 9th episode. Still, quite good to watch but don't expect a happy ending.
Ergo Proxy - another dark themed anime. Hard to tell though what was that about to not spoil it too much.
Wolf's Rain - not too much violence there, but its a very good drama and its very sad, so I feel I can mention it in this category
Animes mentioned here that I don't consider as too violent:
DBZ - If you consider it violent, you shouldn't watch any of the animes mentioned in posts here
Claymore - I don't know why so many people mentioned it here, in this anime violence is very toned down compared to manga. The cuts are mostly quite clean, I don't remember anything too hard to swallow in it. And the ending was sooo bad... I highly recommend reading the manga instead though its still on-going.
Baccano - once you know most of those people are immortal it kinda looses its impact. There are tortures scenes though. But if in the end you don't get really hurt can you still call it really violent?
Higurashi No Naku Koro Ni - I watched only the first season, but I don't consider it violent, its just hard emotionally. Mainly about how hard is to change someone's fate.