THE DOCTOR: Amy, listen to me. I am nine hundred and seven years old. Do you understand what that means?
AMY: It's been a while?
THE DOCTOR: Yeah. No! No!
- The Eleventh Doctor and Amy Pond, "Flesh and Stone".
The Doctor isn't confirmed to have had sex, but sexual innuendos have been made, particularly by the Eleventh Doctor in regards to River Song, who is of course his wife, whom he kisses (albeit rather awkwardly on most occasions, notably "Day of the Moon"), and hints at having sex with. The Doctor is largely asexual though, not understanding why a liquid that hides all non-organic water should be used in swimming pools in "Dark Water", and saying 'you're a beautiful woman probably' in "City of Death" . The Eleventh Doctor one one hand doesn't understand why bunk beds are a bad idea for Amy and Rory's room, but kisses Tasha Lem in "The Time of the Doctor", and the Fourth and Eleventh Doctors have made sexual innuendos and jokes. Susan is his granddaughter, so he presumably had sex, but it is unknown how Time Lords reproduce, or indeed if she's adopted. The Doctor is also strongly implied to have sex with Queen Elizabeth I at some point ("The Shakespeare Code", "The End of Time", "The Beast Below", "The Day of the Doctor").
Outside of the TV series, an unspecified incarnation of the Doctor had sex with Larna, but this could have been a parallel version . "The Dying Days" (Virgin New Adventures novel) ends with an ambiguous epilogue possibly featuring the Eighth Doctor having sex with Bernice Summerfield (an incident seemingly confirmed in "Benny's Story" (Big Finish audio story)) . The Eighth Doctor was probably the least asexual Doctor generally, with his kissing of Grace Holloway of "Doctor Who", generating a lot of controversy, and stating in a novel that he was 'more than friends' with Alan Turing. Also, an erotic novel, The Stranger, featured an amnesiac sexual interest for the protagonist who was blatantly supposed to be the Eighth Doctor. The events of this book were reference in "The Gallifrey Chronicles" (BBC Eighth Doctor Adventures novel), in an attempt to 'canonise' them.
Finally, his half-human clone almost certainly had sex with Rose Tyler, but it is debatable as to whether he counts as 'the Doctor' (although it is worth noting that the 'real' Doctor showed attraction to Rose, before becoming extremely asexual once she left).