Doctor Who: Is The Doctor Gay, Straight, Bi or None of the Above?
Now The Tenth Doctor was as straight as time is not. He carried over his previous incarnation's torch for Rose, and their love story and ultimate parting makes the second series among the best in the whole run of the show. In addition to his growing acceptance of himself as a romantic partner for Rose, he also falls in love with another human, Joan Redfern, and is obviously affectionate towards Martha though he's too beaten up over losing Rose to reciprocate her feelings for him.
Easy fangirls. TARDIS thongs cost money to replace.
The thing is, he obviously wants to. That's the sadness of series three. The Doctor wishes he felt for Martha what she feels for him, and he knows he's hurting her. In the end, he strings her along because he loves her and needs her, but not in that way.
He also shows little or no interest in men at all. Unlike Nine, he is vaguely repulsed by Captain Jack, much to Jack's bitter disappointment. Granted, that has much to do with how "wrong" Jack is as an apparent immortal. Then, he gets hit on by Shakespeare himself. While amused and willing to play along for a joke, Ten is pretty obviously not interested. He is also the most willing to make gay jokes at other people's expense, something Nine and Eleven never did.
It's pretty conclusive that Ten at least was not anything but heterosexual.
Here comes the hard one. On the one hand, Eleven marries River Song (And Marilyn Monroe), and shamelessly flirts with her at every turn.
On the other hand, I think it's safe to say that Eleven is not so much heterosexual and bloody clueless on how to go about any sexuality at all. I like to joke that the parts of his performance Matt Smith didn't life from Patrick Troughton he stole from Anthony Michael Hall in Sixteen Candles. That's an exaggeration, but it's more or less true.
Eleven tends to try and adhere to whatever sexual norms apply to wherever he is, but as he is arguably the worst TARDIS pilot since the First Doctor he usually gets even that wrong by not knowing where and when he is. You sort of get the impression that if he was expected to be gay at any specific place and time he'd go along with it without a second thought, but more of an act of custom than any real sexual desire on his part.
He tends to take a more weird Uncle approach to dealing with humans, as the Second Doctor did, and it's really only because he knows he ends up with River Song after the events of "Silence in the Library" that he seems at all capable of carrying on anything even remotely like a sexual relationship. Though it's clear that he desires to be thought of as handsome, winsome, and other omes, when it comes to actual sexual connection he lacks either Ten's firmness or Nine's flexibility.
He's the Morrissey of Doctor Who is what I'm getting at.