You MUST declare ALL food items. If you enter the country with anything that can be consumed as food, you MUST check "Yes" on your declaration form and be ready to explain and/or show the items to the CBP officers. When I went in for my NEXUS interview, the CBP officer was adamant and stern about it. You don't want to get caught with undeclared items, even if those items would be permitted entry if you had declared them properly.

That said, what you describe--snack items, processed/packaged foods, crackers, etc.--are generally permitted. Again, as long as you declare properly.

Cheese is not a restricted item for the USA as long as it's pasteurized, processed, etc. (home-made goat cheese and some other soft cheeses would be prohibited, though)


Lots of good information here (PDF warning).