Steamed veggies most certainly count. They do not have to be fresh or raw. They can be frozen or canned or fresh.
Tomatoes count as a veggie.
I will let people count romaine lettuce, and other kinds of greens as long as it isn't iceberg. If you have a pre-packaged salad mix that includes iceberg along with other kinds of greens, you can count that mix--but just not pure iceberg.
Potatoes and sweet potatos (yams) are still out. They do have vitamins and minerals, but they are loaded with calories and have tons of carbs/starch. You can still eat them, they just don't count towards your 3 cups. I want people to who don't eat a variety of veggies (especially non-starchy ones) to eat more. We are all adults here. We can eat our veggies even if we don't like them much.
Vegetable juices don't count b/c they are loaded with sodium.
Measure your veggies before cooking them--otherwise you'll have have to eat about double to get your 3 cups. Things like mushrooms shrink considerably during cooking.