Seconding Baccano! and Durarara.

Speed Grapher also fits the realistic world with a darker spin. Mushishi might also be of interest to you, though not every episode is dark (and there is no main plot).

Mononoke- a horror anime. Great artwork

http://en.wikipedia.org/wiki/Mononoke_(TV_series)

Mononoke follows a wandering, nameless character known only as the "Medicine Seller" (voiced by Takahiro Sakurai). The series is made up of individual chapters in which the medicine seller encounters, combats and subsequently destroys various mononoke. The "mononoke" are a type of ayakashi, unnatural spirits that linger in the human world.

The Medicine Seller always proceeds in the same manner, using his knowledge of the supernatural to fend off the mononoke until he can learn the spirit's shape (Katachi), truth (Makoto) and reasoning (Kotowari). Only then can he unsheathe his sword and exorcise the demon.

FLCL (fooly cooly)- only 6 episodes... but every second is gold.

http://en.wikipedia.org/wiki/FLCL

FLCL revolves around Naota. His life is interrupted by the arrival of Haruko Haruhara, who bursts on the scene by running Naota over with her Vespa scooter, then giving him CPR and hitting him on the head with a blue vintage Rickenbacker 4001 left-handed reverse strung electric bass guitar.^[2][3] Later, Naota is shocked to find Haruko working in his house as a live-in maid.

Since then Giant Robots from Medical Meccanica have been coming out of his head and cause more problems for Naota and Haruko. Haruko is using Naota for her search for the Pirate King, Atomsk, which puts her at odds with Medical Mechanica, the monolithic industrial corporation. At the same time, Naota is being watched by Commander Amarao. The Commander believes Haruko is in love with Atomsk and that Medical Meccanica is out to conquer the galaxy. The combination of circumstances gets Naota involved in a three-way battle between Haruko, Amarao and Medical Mechanica.

Berserk

http://en.wikipedia.org/wiki/Berserk_(manga)

Berserk's setting is inspired by medieval Europe. It centers around the life of Guts, an orphaned mercenary warrior, and Griffith, the leader of a mercenary band called the Band of the Hawk (鷹の団, Taka no Dan^?). As he ages, Guts changes from a solitary boy into a man who realizes the value of camaraderie. The story contains elements of both fantasy and horror, as it explores both the best and worst of human nature. Both the manga and anime are noted for their heavy violence.

Samurai Champloo

A young lady named Fuu is working as a waitress in a tea house when she is harassed by a band of ruffians. Another customer, Mugen, offers to take care of them in exchange for food, but ends up instigating a brawl. Jin, a stoic young ronin in samurai garb, enters the tea house in the midst of the fight. Mugen attacks Jin after he proves to be a worthy opponent and they begin fighting one another, ignoring a fire that started during the brawl. They both faint from smoke inhalation. When they awaken, they find they have been arrested for the murder of Shibui Tomonoshina, the magistrate's son who had burned to death in the fire, and are to be executed. With help from Fuu, they escape and Fuu asks them to travel with her to find "the samurai who smells of sunflowers," a mysterious man Fuu can give little description of, but who she insists she must find. They agree to join her, with Fuu making only one condition: they are not to duel one another until the journey is done.

http://en.wikipedia.org/wiki/Samurai_Champloo

Coyote Ragtime Show

http://en.wikipedia.org/wiki/Coyote_Ragtime_Show

The legendary Pirate King Bruce has been killed by Madame Marciano, the boss of the galactic criminal guild. His bequest to his young daughter Franca is ten billion space dollars hidden in a complex custom vault somewhere on the planet Graceland. However, Graceland is now in such a state of civil war that the president of the Milky Way Federation threatens to blow up the planet in a week. Mister, a notorious space pirate, his sidekicks Bishop and Katana, and his longtime rival Swamp must help Franca get to her inheritance before either Madame Marciano and her twelve android Assassins or private detective Angelica Burns get to them.

Okay, I know you said you didn't want any, but there are two Animes before 2000 that you absolutely HAVE to see, no exception because they are absolutely fantastic.

The first one would be Cowboy Bebop

And of course my all time favorite anime, Outlaw Star.

Phantom, Requiem for the Phantom ---------> Awesome...

Dogs Bullets & Carnage--------> good

aoi bungaku--------> A must watch

Yojouhan Shinwa Taikei--------> pretty good....

Shigofumi--------> nice

--------- ----- :3

Animes based in a real sort of world?..

Serial Experiment Lain (13 episode series: 1998)

Akira (movie: 1987) (Can't call yourself an anime fan if you havn't seen this.)

TTGL isn't that good, it has very big things, but that's it (although, up till episode 15 it was  very good)

Man, I haven't gotten one comment on my recommendations...

I don't understand how Code Geass or Alchemist fit in there.

I wonder if Parnoia Agent counts under those circumstances.  Interesting show set in the real world in anycase. 

Second this. 

Arakawa Under the Bridge takes place in the real world from a highly abnormal perspective, and is quite excellent.

Also Queen's Blade (flees).