Specifically, are there any nutritious foods that can be stored exposed to the air, and at room temperature, virtually forever, without spoiling?
Sure. Peanut butter, for example. Pretty much any food which is very low in moisture–there’s almost none in peanut butter, it’s creamy smooth because of its oil content. Also foods very high in sugars, such as honey, don’t spoil as well.
This thread and “Can I prepare for a nuke?” make me wonder if you people know something NPR hasn’t warned me about. :eek:
But peanut butter can mold and the oil will go rancid. And honey, if left open to the air, would eventually solidify (and probably gather any flying critter that happened to visit your home).
If the stipulation wasn’t ‘open to the air’ then I imagine you could keep dried fruit and veg for a very long while in jars. But I can’t imagine anything that, left in the open air, won’t go stale or dry out. I suppose you might be able to keep whole-grain (since it needs to be ‘nutritious’ melba toasts sitting on a plate for a long while but even they would eventuallly get too hard and dry to eat, I’m sure. I guess you could keep dried soup mix open for quite a while but it wouldn’t be much fun to eat.
Water?
I specifically looking for non-spoiling foods that have some significant (ie “nutritional”) measurable caloric content otherwise water and salt could keep almost indefinitely. although water would eventually evaporate.
Anything with grain in it, whether the whole seeds or something baked with grain, that is stored open to the air will eventually have meal moths (grain moths) happily colonizing it. For example, your ship’s biscuit might technically keep forever–but it’ll have weevils in it.
Does water have any actual nutritional value? (Not being snarky, I really don’t know.)
I know water left sitting for long periods of time will get kind of stale and/or murky, but I don’t know if that’s inherent to water itself does or if that would be due to exposure or contaminants.
Protein! 
I remember reading (and this was about 20 years ago (the vast majority of my lifetime) that “honey found in the tombs of the Egyptian pharaohs still tastes good” (yes, that’s verbatim - odd what sticks in a youngster’s head for the rest of his life). I agree that honey tends to dry up and form funky crystals around the lip of a honey jar, but I wonder if a clay pot wouldn’t be adequate to more or less fulfill the “immortality” tag.
I find that I can keep Wasa bread around for a really long time in the cupboard with the bag open with no ill results. Stuff tastes stale when it’s fresh so you don’t really lose any flavor…it’s sort of like a fiber-y Styrofoam on which to transfer peanut butter and other condiments to one’s mouth.
But as for bugs, I dunno. I’ve only managed to keep it around for maybe 6 months.
Bolding mine. As previously mentioned, exposure to the air is the dealbreaker. It’s easy enough to seal a food container, and practically speaking there’s no reason not to. Makes me wonder why that condition was chosen.
I am to guess this statement is from a man who’s never eaten old peanut butter?
(insert pukey smile)
I have a hard time keeping honey for more than a year or so (I don’t eat much of the stuff). It gets crunchy and starts to taste funny. I don’t know if it’s spoiling, but it isn’t good to eat.
If your honey crystallizes, you can heat it (microwave or placing the jar in a pot of boiling water, half submerged) and the crystals will melt, rendering your honey liquid again.
I was trained to tell customer, back when I sold honey in a fruit&veg store, that if your honey starts to go bad from age just place the jar in a bowl of hot water, and it’ll be good as new. This thread just reminded me of a question, think I’ll go start a new thread.
OK - Pure sugar. Just keep it dry.
Christopher Lambert? Shouldn’t be too bad if you boil him long enough.
How about Fruitcake. This one is 125 years old.
How long will prosciuto or salami last if unopened?
That explains a lot.