Many foods naturally come with a little bit of sodium, but sodium-free and very low sodium snacks are available at grocery stores. Some foods, such as nuts and grains, including corn and potatoes, do not contain any sodium.
Almonds, pecans, pistachios and hazelnuts are readily available at grocery stores and contain no sodium at all. If popcorn is air-popped with no-added butter or salt, it is also a sodium-free snack. Fresh fruits and vegetables contain negligible amounts of sodium, if any at all, and they make good snacks as well.
A number of manufacturers make low-sodium processed snack foods. Garden of Eatin' and Bearitos make corn chips with no sodium. Snyder's of Hanover make an unsalted potato chip with no sodium. A brand named Hol-Grain produces Whole Wheat Crackers with no sodium. Matzo makes a no salt added version of their matzo bread that is sodium-free.
For people on a low-sodium diet, the U.S. Department of Health and Human Services department recommends foods that contain less than 5 percent of the daily value. Suitable snacks are often labeled with "no salt added," "low sodium" or "reduced sodium." Less than 24 mg. of sodium is usually noted as zero percent of the daily value on nutritional labels.