My kids seem to eat constantly -- but my son is thin as a reed and so I chalk that up to fast metabolism. My daughter is small for her age and also pretty lightweight, so I don't mind getting lots of healthy food into them.
I try to get them to fix their own food and clean up after themselves, and to stick to healthy foods as much as possible. DS can fend for himself quite well at 8, dd can manage quite a bit at 5, but can not use the microwave or toaster, and can't pour drinks from heavy containers.
Some of my favorite healthy snacks for them are:
Strawberries in season (my dd was stunned to learn that strawberries are good for her body, she thought they must be an indulgence because they are so yummy
Toast with jam (in our house this is NatureBake 100% whole wheat all natural bread with Smuckers 100% fruit jam)
Nancy's honey yogurt (they eat it plain!
Not so healthy but not toooo awful snacks include light salami, deli turkey, and natural Cheetos.