DARK anime with a gripping storyline and perhaps a romance.?

Try watching these, I really like them.

Rainbow: Nisha Rokubou no Shichinin.

Seven teenagers in 1955 have to learn to live together in the same hold in the reformatory of Shio. Confined in a hall where suffering and humiliation are daily, they are waiting for a ray of hope in a dark, incarcerating world. The story follows their life together and how they move on afterwards.

Texhnolyze.

In a man-made underground society, descendants of a banished generation vie for control of the crumbling city of Lux. Ichise, an orphan turned prize fighter, loses a leg and an arm to satisfy an enraged fight promoter. On the brink of death he is taken in by a young woman doctor and used as a guinea pig for the next evolution of Texhnolyze.

Senkou no Night Raid.

The year is 1931. The city is Shanghai. Ten years before America will enter World War II, the hydra's teeth planted by the first great global conflict are beginning to germinate. Hatching like spiders, they weave the complex web of plots and conspiracies destined to inevitably draw entire nations to the brink of destruction. Caught in the heart of these webs, desperately seeking to separate lies from truth, is "Sakurai Kikan," an ultra-secret intelligence agency staffed by extraordinarily talented individuals with abilities far beyond those of normal humans.

Speed Grapher.

Saiga, once a war photographer, works for Hibara Ginza in the capitalist state of Tokyo. Heinfiltrates the Roppongi Club, a secretive base located in the red light district of the city, to collect information about them. However, he was caught in the process and brought forward to a girl called Kagura who was in the midst of a ritual. His contact with Kagura awakens his special ability: the power to make things explode when photographed. In order to unravel the mystery behind the Roppongi Club and Kagura, Saiga begins his solitary battle.

Shinrei Tantei Yakumo.

In order to help a friend possessed by a spirit, Ozawa Haruka knocks on the door of her university's movie research association. There she meets Saitou Yakumo, a rude, unkempt young man with a red left eye, who is said to have spiritual powers. At first Haruka is skeptical, but she comes to believe him when he conveys messages from her older sister, who died when she was a child. Together, they work to shed light on the terrifying events happening at their university. But this is only the prologue of what's to come...

I would highly recommend Puella Magi Madoka Magica. It's a little new, I had to torrent download it to get it (living in the states makes it hard to find anime sometimes...).

The series may be a magical girl, but the series is NOT cutesy or happy in the least. It is considered a horror and a tragedy anime. Normally, I am extremely, and I mean EXTREMELY against magical girls (and ecchi, harems, and slice of life), but this series, even being a magical girl, is my second favorite anime I have seen (first goes to Elfen Lied). It's animated like a cutesy magical girl anime, but with a story and pessimistic air to it similar to Neon Genesis Evangelion (I recommend watching Neon Genesis as well). Just give it a few episodes, and you'll see what I mean.

My favorite dark romance anime is Ayashi no Ceres (Ceres: Celestial Legend). It definitely fits your request decription...but not only does it have a good plot, but a great plot. The art is awesome, all with a lingering supernatural feel. I highly recommend it, Ceres seems to be exactly what you are looking for.

Bleach is good,but only at times is dark, but mostly is a bright comedy action, same goes for Fairy Tail, but if you just want that dark mood the anime called "Darker than black" might fit the bill.

Have you seen Makai Senki Disgaea?

http://youtu.be/6zokOLzDiD8