The list of anime I have watched is over 80 at this point, I don't know what to suggest since I don't know your preferred genre/style yet.

So I'll just tossing out some that I like.

1-Samurai Seven, based on the old western movie "The Magnificent Seven" but with dramatic sword fighting and men turned into machines.

2-Jormungand, the tale of an arms dealer which is mostly given from the perspective of a child soldier she hired as a bodyguard.

3-Baccano, a tale of avarice, cruelty, and immortality set in America in the early 1900s. If you haven't seen this, it's a must watch if you're a fan of Durarara.

4-Durarara, if you haven't already seen it, is about strange happenings in the Japanese city of Ikebukuro which include a Headless Horse(wo)man and an impossibly strong Russian sushi chef.

Edit: This is assuming you've seen Darker Than Black, and Death Note. The latter of which seems extremely safe as a conclusion.