I would say that the number one problem/concern that parents have asked me for help with is: How do I deal with a picky eater? (or: How do I get my kids to eat more veggies/fruits?) The number one way to get kids (or anyone really) to eat new things is to keep introducing different foods into your diet. Sometimes up to 15 times (seriously!). It can take that long to acquire a taste for a new food.
As a kid, I refused to eat macaroni and cheese for YEARS because my first introduction to it was at a daycare that served hot lunches, and it smelled awful to me. Same with tomato soup. And mushrooms (To tell the truth, it took me over 30 years to find a way I liked them). Eventually, I loved these foods, but it was only after I was able to try them myself.
On the other side, I don't advocate forcing your kids to eat foods they don't like. In my classes, we have a rule that everyone tries 2 bites of everything we make. I think that's enough for them to make an effort, but not turn them off of the food entirely; and it usually works pretty well. I've had parents who are completely shocked when their kids come home liking sushi- when before that was never an option.
For me, what has been most successful has been to get kids to make the foods themselves. If they are more involved in the process, they'll be more willing to try the foods you're introducing. Even younger ones can get involved; especially if they see you cooking, they will want to cook too. (It's the same way with anything really... if your kids see you reading, they will want to learn to read too.) If you show them that cooking and eating different foods is important to you, it will be interesting to them.
You can also try adding more vegetables to things that you already know your kids like. (Add peas, zucchini, carrots to pasta dishes, or grill up some onions, peppers, and zucchini with your tacos.) There's a book called Deceptively Delicious by Jessica Seinfeld (Jerry Seinfeld's wife) that specializes in adding fruits and vegetables to foods by pureeing them and sneaking them in there. Personally, that seems a bit time-consuming to me, but there are some good things in there and it's worth a look, if your kids/family is particularly adverse to trying new things.
Some healthy snacks you can add to your repertoire:
-Veggies with hummus
-Pitas with cheese and tomatoes or cucumbers
-Fruit salad; you can arrange it in different ways, like a smiley face or an animal
-Toasted tortilla triangles with cinnamon and apple slices (Cut up tortillas, spray with olive oil or cooking spray and sprinkle with cinnamon sugar, bake in toaster oven or real oven @350* for 8-10 minutes.)
-Edamame (fun to open and eat!)
-Cottage cheese with fruit- they can choose different kinds, like a sundae
-Quick breads; apple, carrot/raisin, pumpkin, cranberry/walnut, zucchini- the possibilities are endless!
-Yogurt dip with veggies (you can add some herbs to the yogurt, or curry powder, or grate some cucumber into it for tzitiki sauce)
-Roasted chickpeas (Place onto a greased cookie sheet, sprinkly with salt, pepper, and other seasonings you like, bake @350* for about 20 minutes.)-- I usually use some cumin and chipotle seasonings. You can eat these by themselves, or in a salad for a little crunch.
-Smoothies- You can hide a lot of stuff in there! :)