Dr. Remy Hadley
Dr. Remy Hadley (Olivia Wilde) is best known as "Thirteen" due to her number card during eliminations for the fellowship. Her mother died when she was young as a result of Huntington's disease, a genetic illness which a child of a victim has a 50/50 chance of contracting. In the season 4 finale, she tested herself for this disease and the result came back positive, meaning that she does in fact have the disease and can expect to deteriorate and eventually die as a result of it.
When House had to choose between the people he wanted on his new team, due to Cuddy making him take Foreman back, he eliminated Thirteen. Cuddy then played right into his hands by saying that he can't have an all male team and he had to hire Thirteen as well.
Thirteen is the only currently-known doctor on the show that is not heterosexual; her bisexuality has been explored since the episode "Don't Ever Change." Dr. Foreman was the first character to judge her as such; House arrives at the same conclusion at the end of the episode. She has since made various jokes about dating girls while refusing to confirm or deny her sexuality. Although fairly ambiguous in the show, Olivia Wilde has confirmed that Thirteen is indeed bisexual in a July 2008 interview.
Hadley's compassion and care for others is one of her best traits, but she has major problems dealing with death and patients that are terminal, perhaps out of fear of her own mortality from her Huntington's disease.