When I was a kid I wasn't a fan of cooked vegetables, though I liked eating them raw, especially served as crudites with ranch dressing. I also didn't like unprocessed or raw tomatoes back then, but I do actually enjoy them now, provided they're accompanying something else.
I am a huge fan of cooked asparagus, broccoli, and brussels sprouts, though I will admit that I probably negate some of their health benefits when I drench them in butter and salt. A lot of people don't like these particular vegetables because they are put off by their flavor, but I find their flavor to be quite pleasant.
I also love things made with hot peppers, even though I do sometimes find the heat to be overwhelming. The flavor they have is awesome, and the challenge of withstanding the heat can definitely be a thrill, though unfortunately my digestive tract thinks otherwise. I didn't have this problem as much when I was younger, but over the last few years I've found that my stomach sometimes hurts when I eat too many spicy things.
I'm also a big fan of caesar salad and taco salad, though admittedly it's more for the toppings that go into these salads than the vegetables themselves. The vegetables are good, don't get me wrong, but the toppings (read: unhealthy stuff like excessive amounts of dairy, simple carbs, and meat) really make these salads.
For something a little less conventional, sometimes I like a nice squash cooked with butter or olive oil. It's soft, warm, flavorful, and it has the perfect balance of healthiness from the vegetable and unhealthiness from all the fat.
Avacado is really delicious too, and I especially like guacamole. I like it even better as a nacho dip than salsa.
As for vegetables I'm not a fan of, I don't really like bell peppers, and I don't like eating corn on the cob either. Corn away from the cob is OK, but on the cob it's a hassle to eat. I'm also not as much into raw vegetables as I was when I was younger, though it's not like I don't like them. I also detest olives, and their weird texture and disgusting flavor. It still boggles my mind how a plant that produces such a disgusting fruit, can also produce such a nice oil.
Wow, I just realized, I really like accompanying vegetables with unhealthy crap.