There's a scene in The hungry Earth (series 5 episode 8 or 9, I can't remember exactly now) where a kid quotes Sherlock Holmes. You know, "once you have eliminated the imposible etc.". I loved that, specially the look on the Doctor's face.

Sherlock and the Doctor are very similar since Moffat is the main responsible of the writting in Doctor Who. I can't say now very specific things, but the Doctor says a lot "I'm busy", "shut up, I'm thinking" and things like that. And sometimes he makes very "sherlocky" deductions. I'll try to post some of them, I'm rewatching now series 6 so as I see one similarity I'll try to post it here

every time House shout : "idiot" to his minions.. so Sherlock.. lol

Oh, I think The Doctor und Sherlock are a bit alike in some points.
Like how they get excited over something that's complicated, how they're usually the smartest person in the room, The Doctor is also quite observant and sometimes, as mentioned before, does deductions. I think they both like to impress people ;)

The deduction I found rather sherlock-ish was in "The Eleventh Hour" when the Atraxi started cooking the planet and the sun became all weird and all the people in the little village where Amy and Rory live started taking pictures of the sun with their mobile phones, all except one: Rory, who was taking pictures of Prisoner Zero.

And I guess they both kinda struggle that their "talents" don't turn them into bad guys, because they both easily could be that.
They both have their own morals. For example both of them frequently break into places and don't really care about that

But of course there is one huge difference: Sentiment.
The Doctor is so emphatic ♥

I think the Eleventh Doctor and Sherlock are quite similar, but before Eleventh they were not. I suppose Moffat has a lot to do with this