Darker Than Black - a series about a young man having his history stripped from him and forced to become an assassin. His only comfort is found in a female that is training him, a female that (under the same circumstances) has given up hope on recovering her past, she is hopeless & has dropped all the weight of emotion,.. Until she begins accepting his affection.
Elfen Lied - a very dark and grissly tale of a girl that has known mostly a life of constant pain, under the microscope of scientists trying to figure out her supernatural details. She manages to, through a series of events, lose her memory & become a sweet young girl that slips into a harem situation with a boy that just happens to have been a childhood friend from long ago. Now she has military personnel hunting her down & she has only her new friends to depend on.
Fruits Basket - a family with a curse that has them turning into zodiac animals meet up with a sweet young girl that, through love, might just be able to end said curse.
These series are "dark" yet find themselves driven by romance.