Vegetables are some of the lowest glycemic index foods that we have available to us. Most vegetables glycemic index is around 20 or less, the majority being around 15. Since most are encased in fiber, you can eat unlimited amounts of most vegetables.
Asparagus, zucchini, broccoli, cauliflower, cucumbers, lettuce, and spinach are all very low glycemic index foods. You can eat as much of these as you'd like. They are free!
As an example, in order to eat 20 grams of carbohydrates from broccoli, one would have to eat over 20 cups of broccoli, which is nearly impossible. Further, the broccoli is covered in so much cellulose (fiber) that it'd be nearly impossible for your stomach to get the sugars out of the broccoli and would not raise your blood sugar.
Some vegetables are higher in carbohydrates and have higher glycemic indices. These are "starchy" vegetables. Corn, sweet potatoes, yams, carrots, beats, parsnips, peas, rutabaga all have glycemic indices that are much higher and should be avoided.