Honestly, I never really had a problem with my kids not wanting veggies. So I can't say that I identify with those moms who wail to me "My kids don't like vegetables. How do I get them to eat them?"
I think it begins very early in life. So, for those reader with babies, or maybe those who don't even have children yet, take heed: feed your babies veggies before fruit.
That was the advice I was given when my eldest son began to eat 'real' food. After we'd done the infant cereal thing, and were ready to move on to things that didn't bear a resemblance to wallpaper paste, I was told to introduce all the veggies first, then let him taste fruits. The basic idea being that fruits are sweet. Veggies, by and large, are not sweet. Therefore, if you give a baby sweet stuff first, he will instinctively like it better than the blander or not so sweet foods. If you want a kid who eats anything, save the yummiest tastes for last, and make them 'dessert', so he gets a chance to like the not so lovable veggies.
Now, it's been probably at least twelve years since I've looked at the offerings in the baby food aisle of the grocery store. Haven't known too many babies in that time frame, and haven't gone down the aisle just out of curiosity. But, from what I remember, the pureed veggies in tiny jars with labels bearing smiling baby faces on them go something like this:
Do they still make baby food spinach? I always thought it looked like pond scum back in the days when I had toothless kids sucking liquefied veggies off the tiny rubber-coated spoon I was wielding. But they all loved it, so who was I to tell them it looked disgusting? And they all ate spinach in it's normal leafy form throughout their childhood without much complaint.
If you are willing to puree your own veggies, and cook them without salt or other seasonings, you can greatly expand your baby's repertoire. I made baby food broccoli. Baby food corn. Baby food rutabaga. And mashed potatoes, well, they're pretty pureed all ready, so just don't add the butter, milk, or salt to Junior's portion. The way I saw it, any veggie I ate, my baby could eat if I left it as natural as possible and made it smooth enough to be swallowed sans chewing and not choke. (Not a vegetable, but I also fed my babies venison. Cooked well and put through the blender, they absolutely loved venison at ages as young as 7 or 8 months!)
But what if it's too late for that? What if your kid is no longer a baby? If they are under about age ten or so, here's a tactic for you: let them smother their veggies in ketchup or cheese sauce or even ranch dressing if they prefer.
Yep. I don't know why, but it seems like all kids love ketchup and they love cheese sauce. Quite a few are fond of ranch dressing. So, I used those substances to my advantage. Don't think you like broccoli or Brussels sprouts? Douse them in cheese sauce. Peas are good this way too. Your kid loves ketchup but refuses green beans? Let them make their beans red and taste like ketchup. Won't eat carrots without ranch to dip them in? Have at it.
The idea is that they will ingest the veggies because the veggies no longer taste like veggies, they taste like whatever it is they are drowning in: ketchup, dressing or melted cheese. Gradually, you reduce the amount of the masking substance, and they learn that the offending vegetable doesn't taste so yucky after all. And one day, you just happen to be out of ketchup, or cheese sauce, or ranch (oh no! out of ranch? that's a staple at this little place here) and your kid takes a tiny bite of the naked veggie, and lives!!
At least, that is how it played out at my house. That's not to say none of my kids ever met a vegetable they didn't like. DD1 has an aversion to peas. DD2 doesn't particularly care for green beans. But they all eat a large enough variety of vegetables that skipping the peas or beans isn't a nutritional disaster.