It depends on your climate, soil, and what kind of shade you have. Is it solid shade cast by a large building, or dappled shade cast by trees? Few edibles will produce in all-day solid shade, but if you have broken shade, or direct sun for at least part of the day, there is hope of getting some vegetables to grow.
Shade is a blessing in hot climates. Areas that get 2 to 3 hours of sun in the morning followed by shade the rest of the day are ideal for growing leafy vegetables during the summer in hot climates.
Here is a list of the more shade-tolerant vegetables gleaned from previous discussions of this question in rec.gardens.edible
GREENS:
ALLIUMS:
HERBS:
LEGUMES:
BERRIES: