Here in our house we have a "snack drawer"  the children know that they can choose anything from this drawer and it will be ok.  I try to keep the junk foods out of the snack drawer, and the adults!  lol.  Usually I keep dried fruits such

as apples, pineapple, apricots, cranberries, and rasins, microwave popcorn in small snack size bags.  Which I know isnt that healthy, but there is 3 kids sharing it so not just one child is eating the fat from this. I stock Granola bars, several different kinds, crunch, chewy with fruit & nuts and without, yogurt covered rasins, trail mix, rice cakes, handi snacks crackers with cheese, and applesauce.  A snack drawer is also a good idea for children who like to pack their own lunch, it is easy for them to choose with out getting permission from mom.  Dont let your kids help themselves all day to this, just snack time. It gives a child a scence of responsibility.  They think they are getting one up on you cause you are not picking for them.  But as the parent you know that they are getting a healthy snack. Its a win win situation! 
 
I have also tried keeping bottled water in the fridge for the kids to help them selves to, that however hasn't worked out as well because they drink  ALOT of water, they can go through 24 bottles in 2 days time, so I opted for refillable rubbermaid sports bottles that we personalized for each child.  Much more cost effective that way. 

Try the snack drawer thing, you will see what  I mean about keeping the adults out.  Once they know it is there they will forgo the chips and salsa and head straight for the kids stuff!