Wow, so many to choose from. I think my favorite food that I link specifically to Christmas & New Year's is egg nog. (The non-alcoholic kind that I make.) Pumpkin pie is also way up there on my favorites list.
Holiday dish that I hate? Hm. I could say "fruitcake," but that's too easy a target. Never been fond of turkey, actually. I prefer beef or salmon for my holiday meals.