1. Attack on Titan - Have yet to see it, but I have gotten some pretty strong good reviews. People fight against giants who eat people. Apparently so twist-filled you can't even look up the wiki without being bombarded with spoilers. o.o
2. Mirai Nikki - A boy get a device called a Future Diary and winds up in a contest to become the next God. There's a girl who follows him around who's... um... crazy in love with him, to put it mildly. I read the manga and enjoyed it very much, anime seems pretty good. It is hard to describe this one without spoiling too much.
3. Gambling Apocalypse Kaiji - Guy is forced to go on a crazy gambling cruise to pay off a debt to loan sharks. The animation style is definitely not your typical anime, and the hard angular style is not for everyone. However, the story is excellent and thought-provoking. The first arc involves a lot of plotting, alliances, and betrayal. The second arc is pretty intense, with several life-or-death situations and quite a bit of violence.
4. Baccano - Seeing Durarara mentioned reminded me of this one! It takes place in the 1930s aboard a train, and the story revolves around multiple viewpoints as to the events that occurred on the train. There is also immortality and lots of crazy people running around.
As far as adding to your list of anime to see, I can also second the recommendations for Cannan, Baka and Test, as well as Fruits Basket and Durarara.