Yes, as said in the Doctor's Daughter and other Doctor Who episodes, he had a wife and family, along time ago when he was living on Gallifrey. He has also been depicted or indicated on numerous occasions as being in a romantic relationship with River Song ("The Impossible Astronaut", "A Good Man Goes to War", the DVD mini-episode Last Night, and "The Wedding of River Song"). In his John Smith incarnation he was unambiguously in love with Joan Redfern in the two-parter "Human Nature"/"The Family of Blood" (however, from a purely technical standpoint he was not the Doctor at that moment). His relationship with Madame De Pompadour in "The Girl in the Fireplace" also had romantic overtones. These examples refer to the TV series only; the Doctor has had romantic relationships in some of the original novels (including the original version of "Human Nature").