Gantz. Absolutely, Gantz. Don't watch it as an anime though. The anime is really short and diverges from the manga a bit.
Seriously, read the manga. It goes on way past the anime anyways. Much violence, much death. All seriousness. If you thought Hunger Games was good... this is on a whole 'nother level. They're trapped in a death hunt where they are summoned to kill aliens hidden among the world in one way or another. It's run like a game by unknown entities for unknown reasons, but when the people around you die, it takes a toll. http://en.wikipedia.org/wiki/Gantz
Other grim, serious anime...
There's Hellgirl (Jigoku Shoujo). When people are abused and cornered enough, they can call on the Hell Girl to take their tormentor's soul down to hell and out of their life immediately. However, in return, their own soul goes to hell whenever they die. The first 4 or so episodes go through wrenching stories of people who have called on Hell Girl. After that, apparently, it changes to focus more on the hell girl herself. I only got so far in before I wasn't able to watch anymore because nowhere to watch it, etc. I need to pick that one back up myself. http://en.wikipedia.org/wiki/Hell_Girl
On a serious note, but not really anime related is There Will Be Brawl. It's a live action web series of an adult themed, dystopian Mushroom Kingdom, years after Mario and Luigi saved it from Bowser and the glory and memory of their deeds has faded. It puts a unique spin on the characters within Super Smash Brothers Brawl, acting and colliding within this dark premise. You won't regret watching this. http://therewillbebrawl.com/episodes.php