As usual, I'm going to take the old school route cause your modern anime with its Moe and magic and ninja death gods frighten me...

I'd recommend:

Last Exile - Awesome steampunk series about flying and revenge.

Haibane Renmei - Incredibly good series about a group of people born into a world with ash wings. Despite its fantasy premise its actual low key and more about character development. There really are no super powers or magic to speak of but its a delightful series nonetheless.

Patlabor movies - Despite its use of Mecha and the third film having a monster, these films are way more about the crime drama itself and features a great cast of characters.

Night on the Galactic Railroad - One of my favorite films of all time, its animation is pretty old (1970's) and its cast is filled with animal characters but the story and the themes it expresses are far from "childish" its ending is really heart wrenching.

Anything Leji Matsumoto - Galaxy Express, Captain Harlock, Galaxy Railways, Queen Emeraldas. Really this man knows how to create a true Space Opera.

Robot Carnival - A collection of short stories done by different animators who were famous back in the 80's. Obviously the theme is about robots and while their are a few really funny episodes, some of them are incredibly touching and thought provoking.

Millennium Actress - Not exactly dark but a great film about an elderly actress reliving her past to a bunch of news reporters and her tale itself begins to come to life around them.

Hope this helps a little.