Of course they've never shown the Doctor, or anyone else, having sex on the show.
But they have implied that the 11th Doctor either has had or will have sex with River Song, his wife and recurring companion.
It's also pretty likely that the meta-crisis clone of the 10th Doctor has sex with Rose at some point after being left in a parallel universe with her by the 'real' 10th Doctor.
In the novels, the 8th Doctor had sex with former 7th Doctor companion Benny Summerfield.
Also in the novels, in what was probably an alternate timeline, some incarnation of the Doctor had sex with the Time Lady Larna, who was effectively his companion at the time.
The 10th Doctor is very strongly implied to have had sex with Queen Elizabeth I.