In the episode "World War Three", Jackie asks "What does he eat?"
There are quite a few food references in Doctor Who. (I will only reference new-Who as I am unfamiliar with older material.)
We can talk about the use of banana (9 uses it several times, 10 invents the banana daiquiri) or his hatred of pears.
We can also note that the TARDIS has been used by Clara as an oven to cook a turkey, with complicity of the Doctor.
Do we have any indications concerning the Doctor’s dietary regime?
As early as 1963's The Daleks, the Doctor is seen eating pretty much what everyone else is eating. At that time, the TARDIS had a food machine that produced little blocks that could be made to taste like anything you dialed up on the control panel, with the one explicit example in that story being bacon and eggs.
In The Two Doctors, written by outspoken vegetarian Robert Holmes, the Doctor himself elects a vegetarian diet after the events of the story, which included a humanoid alien who was deeply interested in cooking and eating the Doctor's human companions. Earlier in that episode, however, he's fishing, and plans to eat what he catches (he fails to catch anything worth keeping).
By the first season of the revived series, the Doctor appears to have reverted to omnivorism, as he has a steak with Rose, Mickey, and Captain Jack in "Boom Town". Certainly, fish fingers would not be vegetarian ("The Eleventh Hour").
tl;dr - The Doctor eats food - what food he eats varies by regeneration.
With each regeneration, The Doctor's taste in food and drink varies wildly. Three was an avowed wine connoisseur, while Eleven spits his wine back into the glass when they're all out at a picnic at Lake Silencio. Ten hates pears, and Eleven finds out suddenly that he hates apples.
There's a remote chance that The Doctor does not need to eat at all - being alien, not to mention one whose body can regenerate using a massive amount of energy, more than could be obtained by even the finest of dinners, he may do it simply because he likes to. That, more than anything else, is likely why Jackie asks what he eats.
In episode 1 of matt smith in the eleventh hour the doctor eats fish fingers so he must eat human food.
In "Midnight", the 10th Doctor eats complementary food that he thinks is both chicken and beef. In the 10th Doctor episode with the 2012 Olympics at the end he eats a cupcake with edible ball bearings. In the 9th Doctor's story "The Empty Child" he does grab some roast beef but is disappointed it got taken away because he was greedy and took two slices of beef.
