I didn't care much for many veggies when I was younger, but I discovered years ago the reason was because I was brought up on overcooked veggies. My mom would always let the brocolli boil for 10-15 minutes. Yuk!
For things like brocolli, cauliflower, or grean beans, if you first boil the water, then throw in the veggies -- wait until the water reaches a boil again, <u>and then count to ten</u> (this part is critical, seriously
), you'll get delicous vegetables. They'll still have all (or most) of their nutrients, and won't taste putrid or bitter.
You can try shredding some cheddar over the brocolli or cauliflower when still hot so the cheese melts, or some grated parmesan (especially for the cauliflower, not so good on brocolli I find). Green beans are delicous in butter with a squirt of fresh lemon juice.
My personal favorite is brocolli stalks. Just skin the stocks, and dice into 1 inch long chunks, boil with the other veggies as described above, and you get tasty, crunchy, morsals -- also good in butter and lemon.