It's basically been debated by rabbis for the last 500 years. (Rabbi Mordechai Willig shlit'a writes about this in Beis Yitzchak in Hebrew a few years ago, and in a very recent YU-to-go journal (in English) related to dating and marriage.
The Gemara says if a parent says "I know you just found Joe Schwartz's wallet, but don't return it to them!", the child should ignore the parent because returning a lost object is a mitzva. But if it weren't, that would imply the child would be obligated to follow an arbitrary request. Ritva challenges this and says no, arbitrary requests are never required! The Gemara meant a case where the parent was saying "Joe is getting on a plane to Japan in an hour and never coming back and will be unreachable forever, but I really really want you to spend the next hour cooking me dinner." Cooking your father dinner is generally within the requirements of honoring him, but not in this case as it conflicts with the mitzva of returning lost objects.
Maharik (responsum 166, though numbered differently in some editions) rules similarly, that among the reasons why a parent can't veto their child's choice of spouse is that "don't marry her" is arbitrary, not "honor me" per se.
Rabbi Willig (yutorah mp3) says personally he's a "maximalist"; Rabbi Hershel Schachter (another yutorah mp3) has stated he finds all three of Maharik's arguments (the above plus two others) to be binding, which thus makes him a "minimalist."
The other huge issue is that even maximalists only go so far. The Gemara says you must feed your parent, but it comes out of your parents' funds, not yours. The parent can't keep demanding money. Thus Rabbi Willig explains the child must accommodate only "reasonable" requests. How to define reasonable, well ... good question.