I frequently camp high in the mountains for extended periods of time. I dehydrate and can a lot of foods and have a few freeze dried meats, but I also carry a number of fresh fruits and vegetables along with tortillas, eggs, cheese, and butter,etc.
Apples, oranges, grapes, kiwis, tomatoes (the little ones in the boxes last longest), peppers, onions, garlic, celery, full sized carrots, potatoes, heads of lettuce and cabbage are some of the fresh stuff I usually carry. The vegies with root bottoms like lettuce and celery, I trim the end and put a damp paper towel against it, then put it loosely in its bag. Scallions will grow in a cutoff water bottle with a damp paper towel in the bottom. I did mention potatoes as a possibility, and I have carried them at times, but I find I use the dried ones such as mashed potatoes, hashbrowns, and scalloped potatoes more often.
I have two mesh hammocks that the fresh stuff swings in. I will sometimes put a damp car towel over the hammock for a little humidity and cooling. The hammocks keep the vegies from being beaten to death when I move my camper on washboarded roads. And they seem to last longer in them than on a counter. So far I have only had to discard a few bruised outer leaves on the lettuce heads.
Some loaves of bread and bagels will also keep for an amazing amount of time. Preservatives! Although with some simple staples such as flour, yeast, baking pwd and baking soda, I can make or "bake" lots of pan breads, muffins, and even cookies and pizza on the stove top.
Some others I haven't seen mentioned are tofu, crackers, cookies, peanut butter, jams, Parmesan cheese, and drink mixes. You can even get powdered or dried hummus and refried beans, You can also buy powdered buttermilk, sour cream, blue cheese, and salad dressings. The powdered buttermilk, sour cream, and even the blue cheese pwd add some nice tang and taste to many dishes. Also ketchup, mustard, vinegar salad dressings, soy sauce, and some pickles and relishes, along with some other condiments don't need refrigeration.
I buy mayo and bbq sauce in the packets. The mayo I don't trust without refrigeration, the bbq sauce I get in packets because I don't use much. I also frequently carry packets of other condiments to add to sandwiches etc when I am out fishing on a river.
I carry a lot as I don't know how long I will be up in the mountains at a time. This last summer I spent three and a half months camping. During that time I got down to towns for shopping only a few times when the smoke cleared out of the valleys for a brief period or two.
Now I have a 46 Engel freezer/fridge that I use as a freezer for meats, some veggies, and a few snacks. It is a luxury to have, but not an absolute necessity. I still don't use a fridge or cooler anymore. Ive found that I really don't need a fridge very often.