There are so many different types of veg and a lot of different ways of cooking and eating them. Keep trying them, a lot of food dislikes are due to early bad experiences (poorly or over-cooked etc). Some flavours need time for your palate to come acustomed to and enjoy, and that takes more than one time of trying something and deciding you don't like it.
Brocolli is one of my favourite veg, but cheese on brocolli doesn't sound too amazing (maybe with Stilton in a soup). A huge mistake with veg is over-cooking it, green veg shouldn't be mushy and soft it should still have a bit of a bite to it. Brocolli is great with soy sauce, garlic, a tiny drop of sesame oil and chilli. Have it with beef, and noodles or plain rice. Sprouts are another pet hate for a lot of people, but cooked right and served with bacon and chestnut, they're wild. Also great in stir-fries.
If you're not into green veg, try things like capsicum peppers (red, yellow) - amazing roasted. Tomatoes, you don't get a more versatile veg (fruit, I know, I know) than tomatoes. Delicious raw with a sprinkle of salt, amazing roasted with garlic and basil on a sheet of puff pasty brushed with mustard or tomato puree to make a really simple tart, or slow cooked into a homemade pasta sauce. Roast potatoes parsnips, carrots with sausages and apple in a bit of cider, a whole meal cooked in one tray, easy and in season now. Try making soups, everything gets blitzed together so that should disguise them! Anything can be made in to a soup by starting with a base of onion and some rice or potatoes, add your veg - something like roast pumpkin, squash, parsnip, carrot, some spices (cumin, corriander seed, fennel seed, bay leaf), some stock and that's it, 15-20 minutes done.
Try, try, try - you don't want to miss out on all those great flavours!