Wandafull - my mum had a very controlling attitude towards food, and as a result, I don't think I learned to regulate my own appetite, even when I was a teenager - and I think I developed a disordered relationship with food.
This was partly because we lived right out in the country, and mum didn't drive - plus this was in the days when shops closed at 5pm, and didn't open at all on Sunday's, and by the time dad got home, it was too late to get to the shops, so she did need to be careful, to make sure we didn't run out of things. But it was even healthy stuff that was rationed - I couldn't have an apple, if I was hungry, for example.
She used to buy Pick 'n Mix sweets - they went into a tin (called The Cough Sweet Tin, for some unknown reason), and dsis and I were allowed one each, each day.
I used to steal food at home - if mum was out in the garden, I would go and pull a bit of cold meat off the leftover joint, or I'd take some cornflakes, to eat dry.
When I left home, and had my own money, and no-one checking everything I ate (she would comment if we took more than the 'allowed' amount of butter or sugar or jam etc), I went bonkers, and piled on weight. Even now, food is a large and unhealthy part of my life - I think about food a lot, and where we will be eating is the first thing I tend to think of, when we are thinking about going somewhere.
I am now horribly overweight (to the point where I HATE myself and how I look, but I still fail, over and over again, when I try to lose weight.
Obviously I am not saying that small children can be in charge of how much they eat - as previous posters have said, children can ask for food for other reasons than hunger - boredom etc, but as others have also said, children do have small stomachs and may need their food intake spaced out over three meals plus snacks - and it is worth remembering that you don't have to feed them lots more food, if you introduce snacks - you can space their food out between meals and snacks. And, of course, snacks don't have to be unhealthy - carrot sticks, cherry tomatoes, nuts, fruit, rice cakes - all good snacks, and healthy too.