For veg, cooked is best as it's easier for them to digest. You can feed carrots, peas, celery, sweet potato, green beans and beetroot. Cauli and broccoli should be fed in moderation as apparently they can cause thyroid damage if eaten in big quantities. I tend to just put a couple of spoons of our leftovers in the dogs' bowls from time to time.
I do feed raw carrots sometimes but more for a healthy treat, frozen in hot weather.