Virtually any type of vegetable or herb should fair well in a container as long as it has enough room. As a general rule, select as large a container as possible. Small containers dry out more quickly and need daily watering. Here are the minimum soil depths for healthy growth. Keep in mind that you can get by with less depth if you use a self-watering planter.
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, rosemary
10-12 inches: beets, broccoli, okra, potatoes, sweet corn, summer squash, dill, lemongrass