My parents went both ways. Coming from a poor farm family, my dad was definitely in the camp of eat what's in front of you and clean up your plate. My mom, on the other hand, was in the camp of only eat until you feel full, because if you eat more than that, you'll feel sick; she was also in the camp of at least giving new foods a try, and if you don't like it, you don't have to eat it.
On the other hand, both of my parents were definitely in the same camp when it came to snacks and such: no snacking before mealtime lest you spoil your appetite.