Most vegetables and herbs do best in areas with full sun (8-10 hours/day). These include tomatoes, peppers, melons, and squash. However, you can get away with a little shade with a lot of crops if you concede that their growth may be less vigorous. Leafy vegetables such as lettuce and spinach do the best in areas with some shade, preferring at least 6 hours/day of sun. Root crops need around 6-8 hours/day of sun. All others listed will do okay in areas with less than a full day of sun, but need to get as close to 8 hours as possible for best results.
Greens: arugula, kale, lettuce, spinach, swiss chard
Root Crops: beets, carrots, kohlrabi, parsnips, radishes, rutabagas, turnips
Misc. Vegetables: beans, broccoli, Brussels sprouts, cauliflower, celery, peas, potatoes, pumpkins, rhubarb
Alliums: chives, garlic, onions
Herbs: basil, borage, caraway, chamomile, chervil, cilantro/coriander, endive, lemon balm, lovage, parsley, sage, sorrel, tarragon, thyme, watercress