You can't beat fresh, local produce. If you can grow your own, we heartily recommend it. Many people, though, don't have the resources to plant and maintain a large vegetable garden.
When you're on a budget, you need to be very careful about the amount of fresh produce you purchase. If your produce ends up going bad before you can use it, you're not saving any money -- in fact, you're literally throwing it away.
Frozen vegetables, though, will last several months in the freezer. Look to store brand frozen vegetables for the lowest prices. A typical bag of frozen veggies will net you six to eight servings, at about 25 cents per serving. If you buy in bulk, your savings will increase even more.
And of course, vegetables are low in calories, high in fiber and full of vitamins.