As was shown in "The Eleventh Hour", the Doctor's tastes change from one incarnation to another. In the same story, the Eleventh Doctor mentioned liking Fish Fingers and custard. Also in the same story, the Eleventh Doctor expected to like apples. He didn't, but the fact that he expected to implied that the Tenth Doctor did.
But if you want a complete list, here you go:
- First: Pomegranates ("The Romans"), Cocoa ("The Aztecs")
- Second: Ice cream ("One Small Step..." (short story)), Lemon Sherbet ("The Wheel in Space"), Patty Cake biscuits ("The Invasion"), Pork, potatoes, carrots ("The Ice Warriors")
- Third: Wine (various), Gorgonzola ("Day of the Daleks")
- Fourth: Apples ("The Pirate Planet", "Revenge of the Cybermen"), Fruicake ("Image of the Fendahl"), Garlic ("The Eight Doctors" (BBC Eighth Doctor Adventures novel #1)), Ginger Beer ("The Android Invasion"), Liqourice Allsorts (various), Bananas ("Death to the Doctor!" (Doctor Who Magazine comic story)), Doughnuts ("The Beautiful People" (Big Finish audio story))
- Fifth: Celery (various)
- Sixth: Gumblejack ("The Two Doctors")
- Ninth: Bananas ("The Doctor Dances")
- Tenth: Easter Eggs ("Planet of the Dead")
- Eleventh: Fish fingers and custard ("The Eleventh Hour", "Let's Kill Hitler", "The Time of the Doctor"), Scones ("The Beast Below"), Jamie Dodgers ("Victory of the Daleks"), Bananas ("Let's Kill Hitler")
Additionally, multiple Doctors have enjoyed Coffee, tea, and jelly babies.
The Doctor has also had his least favourites:
- Sixth: Carrot Juice (various)
- Tenth: Pears ("Human Nature")
- Eleventh: Bacon, baked beans, bread and butter, carrots, yoghurt ("The Eleventh Hour"), Wine ("The Impossible Astronaut")
Additionally, the Eleventh Doctor used to hate apples, but eventually regained a liking for them. 
- ↑ Who-ology, written by C. Scott and M. Wright. Published by BBC Books in 2013.