Generally speaking, most Vegetable plants do best with 5 or 6 hours of direct sun a day. Sometimes it is hard getting any direct sun if your garden does not have a southern exposure. If you can't open the canopy above your garden so that the plants get direct sunlight, then it might be best to look into container gardening, so you can put the plants where the sun hits the most. Around here some farmers rent 1/8th acre plots for $20 a growing season for people who want a vegetable garden but dont have space or some other reason.
The sun is as important to a vegetable plant as soil and water. Without full sun for a minimum amount of time your plants will not only be stunted but the harvest will be smaller. It would be like giving your plants only half of the water it needs, or planting in sand.
Most plants come with a little plastic tab informing you of the maturing cycle. i.e. 75 days, 90 days. I would pick the ones with the shortest cycle, because it is at that point that the vegetable can begin to be harvested.
Regardless of the maturity cycle, the plant would still need sun.
