I was definitely picky, and most of my dislikes were texture (except veggies--my parents used to boil the living daylights out of everything, so they were sad and limp AND tasted awful). I also didn't particularly like milk. Still don't. I've gotten over some of them (runny egg yolks, avocado, pineapple, cherries), figured out how to cook so as to avoid texture/flavor issues (every vegetable ever, onions, beans (sort of)), and some are probably permanent (raisins, peas, summer squash).
My parents did the "three bites" rule. Mom was never too keen about enforcing it with lima beans, though. Turns out she didn't like them either!