Don't have kids myself, but my brother's kids will ask first. They'll ask for graham crackers and they might get them, or they might be told they need to have a piece of fruit first. But they aren't denied food if they are hungry; their parents are just trying to monitor what they eat so they get enough fruit and vegetables. They get plenty of snacks, just not a lot of sugary or salty snacks. I think it started when they were too little to get their own snacks and it has just continued. Their parents don't make a fuss about it. When I'm there, I might be told to make sure to give them a piece of fruit or some carrot sticks the first time they ask, but that's about it.
When I was a kid, I just got a snack if I wanted one. We always had fruit and crackers. No soda in the house, but generic KoolAid type drinks or water. We all knew what was allowed for snacking and what wasn't--those cookies Mom baked that afternoon were probably dessert for dinner and we knew that we were not to touch them. The big note in the cookie tin that said: Do NOT eat! These are for dinner! may have cued us in.
At big family get-togethers, I've noticed young cousins and such asking their parents if they can have specific foods or drinks. Everything will be out for the taking, but they'll ask if they can have a soda or some chips, but not ask if they can have veggies and dip or potato salad.