Some children are extremely resistant to trying new foods. They may need to be exposed to them many times before they will attempt to try them. Do not give up! Serve vegetables with every meal, but do not force your child to eat them. Let him or her decide what to do with them. In the mean time, offer a daily multivitamin to prevent vitamin and/or mineral deficiencies.
I am not a fan of vegetables either and I'm a vegetarian. Thankfully now people have come up with ways to sneak veggies into the foods. Check out The Sneaky Chef section on the home page and you'll find some great Recipes for Your Family! Also, don't underestimate kids, many do like veggies!
Here's a trick that works for me. Cheese sauce: Cut Velveeta cheese into cubes and place in small sauce pot on medium heat, add about 1 Tablespoon of milk, more or less depending on how much cheese sauce you want to make and how thick or thin you want the cheese sauce to be, more milk makes a thinner sauce. Heat together, stirring and serve over top steamed vegetables such as cauliflower, broccoli, brussel spouts, it's very good.
Also, my kids love candied carrots. Peel carrots and cut into coins, steam until tender, but not mushy. Add to a skillet with a little water and brown sugar, gently toss around to coat. Serve.
Also, you can slide vegetables into surprise dishes such as in spaghetti sauce, pizza sauce, tacos, etc. We like to buy soft shell tortillas, spray a bottom of a baking pan with cooking spray to prevent sticking, spoon a little pizza sauce over top shell, top with mozzarella cheese and allow your kids to make their own pizzas by providing them with toppings, such as fresh mushrooms, broccoli florets, green peppers, black olives, ham, even fruit like pineapple tidbits, etc. Creating their own food helps. When they make it, some how it's now something they want to eat. Allow them to help in the kitchen and preparation of vegetables they will soon love them.
Squash, yellow crooked neck or zuccini is great steamed or fried with corn meal. Ranch dressing is also good to serve with fresh vegetables as a dip. You could also make what I call "kids salads" my kids throw together their own salad, but omit the lettuce. You'll be surprised at what they will eat when the vegetables are prepared and ready for them to toss together the way they want. The different colors of the vegetables is exciting for them to play with and then eat. Hopeful these ideas will help. Best wishes!