In a recent study, ten minutes before researchers served lunch to 3-to-5-year-olds, the kids got carrots of varying portion sizes (1 ounce, 2 ounces, and 3 ounces, or no carrots at all.) The results were two-fold: The bigger the portion of carrots, the more the kids ate. And after eating their veggie first course, you might think that the preschoolers who ate the most carrots would pass on the veggie served with their lunch (broccoli) but all the kids went on to eat about the same amount! (Which means that the kids who ate the most carrots first got the most veggies overall.)
Try it! We did -- and were amazed at how successful we were getting our kids to down those veggies. The trick is to give them a veggie first, without any other food offered at the same time. If they're hungry, they'll eat.