I've been watching a lot of Bear Grylls lately - yes, I know it's mostly staged, but I still like it. A few episodes I've watched have really given me that patented Old School Dungeoneering feel. He's out there, ostensibly by himself, and what matters most is his scarce equipment and the kinds of things that the 1e Wilderness Survival Guide and Dungeoneers Survival Guide were full of. Plus, episodes like the one in Romania are full of the kind of terrain that a good fantasy campaign will thrive on.
In this part of the episode, he has to deal with descending a scree slope (now imagine combat on such a slope, where the enemies are at the top!). Then he goes dungeoneering with an improvised torch. Note that the reason he's using the cave in the first place is to save himself from the time, pain, and effort of dealing with the wilderness! Of course, a fantasy cave would never be quite that uninhabited - we'd always put at least one encounter in it - but I think the idea of having a subterranean cavern (with frigid swim at the end) as a means of travel is actually pretty cool. Remember that one of the original inspiration dungeons, Moria, was traversed by the Fellowship of the Ring for precisely the same reason: it was too hard to go any other way.
Another real danger: claustrophobia and panic. Also, don't forget about "rising floodwaters" - lots of game caverns and dungeons have rivers or waterways or flooded sections, but except for the occasional trap, I don't know that I've ever dealt with rising floodwaters as a dungeon hazard. I rather like the idea. If nothing else, it can be used to cut off a party from retreating to the surface.
There's loads more examples I could pick out, but for now just one more:
Hunting bats for food with a vine racket is a part of the 'Forage' skill that rarely gets described in-game, and maybe that's our loss.