I grew up on a rather limited menu, as far as veggies go. The only veggies that ever crossed our plates were potatoes in various forms; salads of iceburg, tomato, and carrot, with cucumber, raw onion, celery, and sometimes radishes on the side; and canned corn and one particular type of canned bean (ranch-style).
When I was in high school, I introduced bean sprouts to the house for cooking stir-fry. My parents make faces or weird noises about a lot of my cooking (mostly noises over the phone when I'm telling them about my experiments) because I'm fixing things like squash, eggplant, and broccoli.
I am picky about a few things. Spinach must either be raw or if its cooked, it has to either be smothered in cheese or be in Greek food. Broccoli and cauliflower must be cooked. Mushrooms must be hidden (I'm at least eating them now, in a very few things, so its progress!). And zuchinni and artificial sweeteners need to never touch my food, they make me sick (which stinks because I love zuchinni).
Luckily, my son is usually happy with whatever he gets fed. Hopefully this lasts even once he realizes how much his daddy turns up his nose at because...
My DH is our picky eater. He wants hamburger helper beef stroganoff, not homemade. He wants mac'n'cheese from a box, with the orange powder. Prefers canned veggies for the few he'll eat (peas and corn are about it). Fruits are just as hard to get into him, so far my only success is with sliced apples and occasionally watermelon. Basically, he wants meat, carbs, and dairy. One of his doctors actually forbade green leafy veggies, due to the Vitamin K content and a blood-clotting issue he has (super prone to them). Oh, my only real "success" with fruits and veggies, are ones hidden in desserts. I had to give up, pumpkin pie/bread totally counts as a veggie when he eats it.
I actually find meals easier when he goes on his "dieting" phase, since he usually does Atkins. Then I just make sure the main dishes are acceptable and round out meals for myself and DS with veggies that he doesn't eat anyway (so healthier for us, while not tempting for him). I'm looking forward to hitting the end of our "pantry challenge" (using up all the boxed junk and non-diet-friendly foods) so that we can move into the "diet" phase again.
ETA: I'm also working on cabbage, slowly, for myself. I love eggrolls, and I have started to find a restaurant or two with coleslaw recipes that I kinda like. DS loves coleslaw so far. Introducing that little guy to foods and trying to make sure he doesn't wind up picky (due to catering, not true dislikes) inspires me to try new stuff. Especially when (like with the coleslaw), I put something I don't like on his plate and he tears into it like its the best stuff ever, I have to at least snitch a taste back.