When you start a new game of Earthbound, it asks you what your favourite food and favourite thing are. Does this actually matter for anything? (I suspect not, considering it is a open-ended question where I can type whatever I want within a 5 character limit, but I am curious.)
They're used in a couple of spots as "flavor text" - your favorite thing will change the name of one of your Psi attacks, and your favorite food will be offered to you at times. (Among other uses for the food you choose, I believe your mother will offer it to you if you return to your house later in the game, and it counts as fully restoring your party's HP and PP.)
Otherwise, they don't impact the story/plot/gameplay in any way whatsoever.