A lot of people, especially in the western civilization, grow up with a disdain for vegetables. If you think about it, vegetables do not taste bad at all but it is the way they are prepared that makes them unpalatable or undesirable.
Just because they need to be mashed up for babies does not mean to continue that trend once we grow older. There are two ways most Americans serve vegetables and ruin not only their taste, but also the nutritional value: Overcooked and topped with useless condiments that add more fat and calories, where it would almost be better to not eat vegetables at all.
The best and tastiest way to serve vegetables and make yourself eat them is to prepare them fresh and serve them as a salad. Don't shy away from trying vegetables that are thought of as unconventional salad ingredients. Again, modern civilization has found ways to ruin salads.
In most restaurants and private kitchens what passes for a salad is a big bowl of limp and often bitter-tasting lettuce, worsened by the addition of soggy tomatoes, with several slivers of carrots. It's no wonder these plain concoctions have to be drowned in an explosion of fatty salad dressings to make them edible.
When making salads, skip the lettuce and use baby spinach instead for your base. Dark green leafy vegetables have many more nutrients than lettuce, especially iron, and spinach is one of the tastiest ones. Most people associate a bad taste with spinach, probably brought on by childhood experiences of being presented with an unappetizing boiled, moss-colored mass.
Raw it actually has a pleasant taste, never bitter like old lettuce can be. Try adding radishes, zucchini, squash, peppers or anything else you can find in the vegetable aisle, but skip the tomatoes. Tomatoes (which are technically a fruit) make salads soggy, but if you like them, use them as a salad topping just before serving.
You can also make a vegetable salad without leafy greens. For example, cucumbers are very refreshing in the summer. You can make a very tasty vegetable dish using diced cucumbers, a can of drained chickpeas, a bit of parmesan cheese, and a couple of table spoons of plain, unsweetened yogurt to hold it all together. Chickpeas are usually thought of as a salad garnish, but they are high in protein and taste very well as a main salad ingredient. If you don't like yogurt, you can use an extra virgin olive oil based dressing instead.
Another tasty way vegetables can be served, especially during hot summer months, is to make a sandwich with them. Lightly butter some rye bread (or any type of grain bread like pumpernickel), top with sliced vegetables, add seasoning of your choice (except for salt) and you have a nice light, sensible lunch.
Radishes and cucumbers work well for this purpose, but you are only limited by your imagination and taste buds. You can even expand and add some turkey or chicken breast if vegetable sandwiches don't sound appealing enough. They key is to make the vegetable the main ingredient, not the afterthought like custom currently dictates when it comes to sandwiches.
An additional way of making vegetables tasty, especially when it comes to serving your family, is to hide them in a main dish. Meat loaves are an excellent choice. Simply chop up an assortment of vegetables in your food processor and add them to your meat. Once the meat loaf is cooked, no one will know that the vegetables are even in there.
To summarize, the best way to make you eat vegetables is to step away from conventional thinking. You can make them the main event instead of an afterthought, and try out new ones that you never bought before.