Virtually any type of vegetable or herb should fair well in a container as long as it has enough room. Small containers dry out more quickly and need daily watering. Here are the minimum soil depths for healthy growth.
4-5 inches: chives, lettuce, radishes, other salad greens, basil, coriander
6-7 inches: bush beans, garlic, kohlrabi, onions, Asian greens, peas, mint, thyme
8-9 inches: pole beans, carrots, chard, cucumber, eggplant, fennel, leeks, peppers, spinach, parsley
10-12 inches: beets, broccoli, okra, potatoes, sweet corn, summer squash, dill, lemongrass