What useful building (could be a house, temple, storage facility, etc.; it counts so long as it occupies human beings from time to time and was built by human beings (so caves or whatever don’t count)) is at the highest altitude in the world?
My guess would be the little shack that serves as a waypoint for travelers heading for Mt. Everest, somewhere in Nepal. It’s been on the Travel Channel a time or two - basically a couple of rooms, a tea shop, and an outhouse.
Any other guesses?
The Sphinx Observatory is said to be the highest-altitude structure in Europe.
Other than that, I gots nothin’.
The Everest base camp in Tibet has a permanent structure at about 5,500m. Perhaps there were higher mining buildings in the Andes?
The University of Tokyo Atacama Observatory is located at 5,640 meters somewhere in Northern Chile.
I wouldn’t be surprised to find that there were even higher constructions in the Himalayas, but my Google skills fail me on that one.
Well. Apparently India has installed a helipad at Point Poonam on the Siachen glacier at 6.400 meters, making it the highest permanently manned post in the world. I imagine that will be tough to beat.
Converting that to “American” it’s like, what, 20 feet. 
Sigh. And I even made an effort to write in “American” in my first post.
Or: At 20 feet, Siachen could be the world’s lowest glacier!
I spent the night at Loboche (16,200’) on my way to the Everest Base Camp and Kala Plater (18,000’+). Sleeping at such a high altitude can be a problem which is why I stayed there instead of the much higher hamlet at Gorakshep, (16,950’). Its the highest place in Nepal where people actually live.
Even when I was there over 30 years ago, both places were occupied year round. I’m sure its still true today.
Up near base camp near Rongbuk (5,100 metres/16 732 feet) there’s a monastery, a guesthouse run by the monks - with holes in the windows - and the worst hotel in the world.
Tibet has some very high monastaries.
Somewhat related: La Rinconada, Peru is the highest city in the world at 5,100 meters (16,732.28 feet). Has 30,000 inhabitants.
I presume the OP is excluding the international Space Station, which is occupied and at a much higher altitude than anything mentioned.
Going once… Going twice…
[Banging gavel]
Sold! to the highest Buddha!
But it’s not “in the world”. Its out of the world.
You! Corner!
To continue the smart-ass-ery…
Technically, most of the buildings mentioned are not ‘in the world.’ To be in the world, we’d need to look at underground complexes built into mountains and so on.
So are we looking for the highest-altitude building attached to the world? 
According to a 60 minutes story(aired 3/9/14) the building at the highest elevation in the world is a railroad station in Tibet. The second is the ALMA radio telescope array in Chile.
But the International Space Station is certainly “attached to the world” – by gravity, if nothing else. I believe they have to periodically fire rockets to maintain their orbit.
And it also is in an (extremely thin) fluid of air up there. Much thinner than the fluid of our oceans, that all the ships at sea float in. Do we count ships as “attached to the world”?
We could play this word-definition game for a while here… 
What, Starbucks missed one?
About ten years ago, I heard some nonsense about somebody wanting to build an actual hotel at the last base camp before the Everest summit (that’s Camp 3, right?) Whatever happened to that plan, as if I need to ask? I mean, seriously—did it go anywhere at all? The notion was that it was actually going to have supplemental oxygen piped into each suite.
