Best=Chocobo Treasure Hunt from Final Fantasy IX. It was fun, you get some nifty items and treasures as well as upgrading your Chocobo and it can quite literally suck a good hour away from the actual quest. "We gotta go save the Desert Kingdom!" "In a minute, I gotta find the Tresure Map to get Blue Chocobo." And after all your hard work, you get the gem that will allow you to summon one of the greater and more awesome creatures in the game.
Worst=Lightning Bolt dodge in Final Fantasy X. I can understand that this mini-game is used to challenge the gamer to get Lulu's upgrade item for her master weapon, but seriously? I have to dodge 200 bolts in a row without being attacked by monsters. Oh, you can have an item called "No Encounter" but the item requirement is so rare you only meet one enemy in the game that carries it and its super rare drop, not to mention you can't revisit said area.
I also laugh at the fact that doing this would get the best weapon fully upgraded in the game...supposedly. I quite literally broke the Sphere Grid and Customization system by getting the same enemies to drop items I needed for 1 MP cost, Double Magic Cast and Ultima for about three different characters, which could deal out 11,000+ damage per spell.