Most non-starchy vegetables are very low in carbohydrate -- less than 5 grams for half a cup worth. But there are differences between them. See this master vegetable list for complete information, but here is a quick rule, dividing vegetables into four groups, depending on what part of the plant they come from. There are exceptions, but as a general rule, this works pretty well.
1. Leaves have the least amount of carbohydrate, and what little there is is wrapped in so much fiber that there is little, if any, impact on blood sugar (this could be helped by the fact that they all contain enormous amounts of vitamin K). They are also rich in phytonutrients, vitamins and minerals. Examples: lettuce, spinach, Swiss chard, herbs. Also, alfalfa and other fresh sprouts (but once you grind up sprouts and pack them together, as in some types of bread, all bets are off, blood-sugar wise).
2. Stems and flowers are next, including asparagus, cauliflower, broccoli, and I would also throw mushrooms in there.
3. Fruits -- and by this I mean the part of the plant that contains seeds. This is botanically the fruit of the plant, although we tend to call it "fruit" only if it's sweet. This includes peppers, squashes of all types, green beans, tomatoes, okra, and eggplant. Avocado is also a fruit, though lower in carbs than the others. Plantains have the most carbs in this category, which makes sense, as bananas are among the highest-carb fruits.
4. Roots and Seeds -- Many roots are very high in carbs, such as parsnips, water chestnuts, potatoes, sweet potatoes and yams. However, some are actually low, such as jicama and radishes. Celery root (celeriac) and carrots are also lowish. Seeds which are vegetables are mainly legumes including peas, and corn.