They love bananas and apples, no pig so far that didn't like them. Every pig has its likes and dislikes - we've had pigs that didn't like sprouts (very intelligent, these pigs were
), others didn't want peppers and so on. One of them would gorge on cucumbers and all other fruit & veg, his brother wouldn't touch the stuff.
As for what they can't have: any catering waste (have a look around this forum for the rules & regulations as they're explained in quite a few posts, basically nothing that's been through a kitchen) and no raw potatoes (pigs can get sick and die), potato haulms and tomato plants (poisonous), and I've been told not to give then onions, citrus fruits or parsnips (pigs get blisters).
Others will add to the list. Do have a look around this forum re feed, alternatives and quantities.