Leafy greens and herbs are champions when it comes to growing in part shade. Their large leaves give them more area to collect sunlight for photosynthesis, allowing them to adapt to lower-light conditions–even areas with just 2 hours of direct sunlight a day or dappled sunlight throughout the day.
Root vegetables like beets, carrots, and radishes, and cool-weather crops like broccoli, kohlrabi, and peas will mature more slowly or roots may be smaller when you harvest, but they adapt well area with less than full sun–3-5 hours.
The majority of fruiting vegetables like tomatoes, peppers, okra, and squash produce best in areas with full sun (6 or more hours per day).
Consider using your shade as a microclimate. Plants grow more slowly with less light so for instance, if you sow lettuce in two areas, one with sun and one in part shade on the same day the crop in the sunny area will mature before the crop in shade giving you staggered harvests. If you live in a hot-summer area, afternoon shade helps keep cool-weather crops like spinach, cilantro, or radishes cool, delaying bolting (flowering which is detrimental to flavor or production). Growing in moveable containers is a great way to start experimenting with shade growing, they make your garden "mobile" allowing you to move crops around.
Plants that can handle shade (2 or more hours of full or dappled sun).
Plants that can handle partial shade (4 or more hours of full sun).
Other Vegetables
Herbs
There is plenty to grow even if you don't have full sun! Try experimenting with growing in shade to see how the results stretch your season or to expand your growing space. What edibles do you grow in part shade? Share your experiences in the comments below.