As noted on the Washinton, DC Department of Health website, most major grocery chains (such as Safeway and Harris Teeter) accept WIC vouchers. In general however, the best way to find out if a particular store accepts them is to either call the store, or the local Health and Human Services department directly as the list of stores varies by state.
While the USDA's WIC website itself does not contain a list of vendors, it can be used to access each individual state's program website, which provides lists of foods that can be purchased with WIC benefits, as well as information on that state's approved vendors.
The U.S. Women, Infants and Children federal program grants money to states to allow low-income families to purchase food from designated stores. It is targeted to breastfeeding, pregnant and postpartum women and their children up to age 5. According to the USDA Nutrition Service, these families are at risk of nutritional deficiencies without supplementary help.