It’s a little easier to talk about the things you can’t bring through US customs.
The United States limits the amount of alcohol travelers can bring with them into the country. You can bring one liter duty-free, and after which a customs duty of 3% per liter is imposed. Tobacco products also have individual limits, typically 200 cigarettes and 100 cigars per person. Anything above that, rather than being taxed, may be confiscated.
Meat and produce are generally prohibited, though there are some exceptions for cured or processed products depending on how they’re packaged. Cheese can be problematic, too.
Plants are a no-no (they might be ferrying unwanted pests), which means some crafts made from plant materials (like woven baskets or hats) aren’t going to make it through customs, either.
Depending on where you’re coming from, some pieces of art may get you into trouble at customs—because the country you’re departing has expressly forbidden items it deems “cultural treasures” to leave its borders.
Check the US Customs and Border Protection list of “Prohibited and Restricted Items” to find out what should (and shouldn’t) be on your shopping lists when you travel.