Vegetable gardening in containers is only limited by the size of the container and your climate. Most often grown in containers are tomatoes, peppers, lettuce, and potatoes. In climates with only light frost and/or an enclosed area (garage) to move containers into when frost hits, you can grow dwarf fruit trees and much more.
Vegetables for container gardens are usually bush varieties bred for compact form, like 'Raven' zucchini. Smaller-fruited tomato varieties like cherry, grape, or salad tomatoes usually perform better in containers than larger, beefsteak varieties, although with the right potting mix and soil amendments, any tomato variety can be grown in pots. Eggplants, peppers, and chiles grow very well in 7-10 gallon pots.
If you're growing carrots in containers, choose "mini" varieties, like 'Babette' or 'Adelaide', or round, radish-style carrots like 'Romeo'.