When my kids were young, I put pureed vegetables (you can puree steamed veggies in a blender or food processor, or use jars of baby food) into spaghetti sauce, meatloaf, burgers, casseroles, soups---get creative!
Another idea is to cook "bitter" veggies (like broccoli, spinach, etc.) in milk, rather than water. I didn't like to simmer veggies in milk, then just throw out the milk (where all the vitamins are!), so I started making milk-based soups with the milk. Creamy broccoli soup was a favorite!
Simmer one head of broccoli (chopped, with some of the smaller stems) and one small diced onion, in milk. Puree in a blender or food processor, add one can (14 oz.) of chicken broth, salt and pepper to taste. If a thicker soup is desired, add light sour cream (1/2 to 1 cup). My kids loved this!
You can also roast many veggies (carrots, beets, red peppers, zucchini, yellow (or summer) squash, onions, mushrooms, turnips, parsnips). The sweeter ones (carrots, beets, red or yellow peppers), kids might eat, on their own. Otherwise, you can puree for soups and sauces, or dice really small and add to things like soup, salad, etc. Go on-line or look at cookbooks from the library, for recipes like roasted carrot and beet soup. Butternut squash and apple soup is another favorite, as is sweet potatoes with apples. Also, many kids will eat tomato soup, vegetable soup, minestrone, etc.
The rule that we had is that everybody had to try it, but if someone didn't like it, they could leave it on their plate or in their bowl. Be persistent, because tatse buds DO change over time! It might also help to read "Green Eggs and Ham" by Dr. Seuss, and remind children that the main character didn't THINK he would like green eggs and ham, but when he tried them, he LIKED them!
Also, salads are often more tolerated by kids, because it's "salad" and not "vegetables"! Make sure you use dark leafy greens, like romaine lettuce, green and red leaf lettuce, baby spinach and spring mix. Add things like cucumbers, shredded carrots, cherry or plum tomatoes, even avocado or jicama. If your child is REALLY resistant to salads, try romaine lettuce (pretty mild) with cucumbers and orange segments (or canned mandarin oranges) and a mild Italian dressing.
Just keep trying! I've read that if you offer a wide variety of FRESH fruits, you can almost duplicate the vitamins and minerals of vegetables, but I would only use that as a last resort!
Keep in mind that 1/2 cup of pasta sauce with vegetables, like Ragu, which has several varities, is a full serving (or more!) of vegetables. (It will say on the front label.) Also remember that "a serving" of vegetables varies with the age of the child! Ask your doctor what "a serving" is for your child's age---it could be as small as 2 Tablespoons! (It's 1/2 cup to 1 cup for adults!)
Also, remember to "model" the behavior---both parents should eat vegetables in front of their kids (preferably at a family dinner!) Hope this helps!
J.