Girls are icky, and the Doctor should have nothing to do with them.
I'd laugh too except that this does actually seem to be the attitude of many fans. (And to be fair for a moment, it's not just Doctor Who. Anytime any ongoing characters in TNG, DS9, Voyager or Enterprise developed any sort of romance you had people responding the same way, usually with some variant of accusing the writers of being immature.)
The fact is you have people who think the Doctor should be utterly asexual, and this list includes some honoured members as Tom Baker. Part of this is a holdover from the now-obsolete view that Doctor Who is a children's program. It's not a children's program and hasn't been since the day the first Dalek menaced Barbara Wright. It's a family program, and as such it opens up the possibility of there being romance between characters. Back in Hartnell's day we saw a bit of this with Susan falling in love (and snogging!) David Campbell, and Barbara and Ian of course barely hid their relationship. And even the Doctor (yes, old grey-haired Billy Hartnell himself) had a bit of a romance going on in The Aztecs.
Those who think the Doctor only just started to notice girls after getting shot in San Francisco haven't watched enough of the series. Watch The Green Death where the Doctor (Pertwee now) clearly shows he has feelings for Jo Grant. And despite Tom Baker's opinion that the Doctor is asexual, there is no denying that sparks flew between the Doctor and both Romanas (even more so with Lalla Ward since she and Tom were dating in real life).
Now that the Doctor is pretty much staying "young" (at least for the fourth incarnation in a row), I don't think it's realistic for him not to have romances from time to time. He's lived too long to not have them. And the fact is we've not seen this as often as critics accuse. Rose Tyler was a special case; Jack and Martha were in love with the Doctor but he did not reciprocate; Donna loved the Doctor but in a non-romantic way. As for others, Joan Redfern was a special case because the Doctor fell in love with her in his John Smith incarnation with no memory of being the Doctor. Lady Christina came on to him, but he never really reciprocated. Really, except for Rose, the only cases of "guilty as charged" is Madame de Pompadour and the off-screen relationship and marriage he had with Queen Elizabeth I as mentioned in End of Time.
We can't count River Song yet until we learn what her story really is.
Matt Smith's Doctor will probably get into romances as well. As long as the stories are good, and remain true to the spirit of Doctor Who, I could care less if he snogs Amy Pond or gets caught in a compromising position with a Dalek...
Alex