Older DD & DS were pretty good eaters (& still are). DD is a little pickier than DS, but there has always been veggies that they've liked.
Younger DS... not so much! And I promise he's been introduced to foods just like his older sister & brother were - I didn't do anything differently w/ him! So I don't know why he doesn't like any vegetables! He loves just about any fruit though!
Occassionally, he will eat the "matchstick" carrots as opposed to the whole baby carrots. Sometimes, he will eat cucumbers & lettuce. However, all his vegetables must be raw. He won't eat cooked. He doesn't like green beans or peas or cooked carrots or broccoli or zucchini or even corn (& I don't really even consider corn a vegetable!).
It helps if he has some kind of dip to go w/ the veggies.
I will sneak veggies in spaghetti sauces & he likes zucchini bread. Additionally, he really likes pasta, so I buy the tri-color pasta that's made w/ spinach & tomatoes.
I just keep putting a taste of everything on his plate & try to have something that he likes on his plate as well. He's picky w/ meats too - he's the only kid I know that doesn't like chicken nuggets! His favorite meal is bacon & pasta w/ some kind of fruit.
We try not to make an issue of it &, again, just keep offering different things to him in the hopes that eventually he'll find some veggies he likes. He didn't use to like cucumbers, but, just within the last couple of months, he's started eating them.
Oh, and I've decided to count ketchup as a vegetable as well!