Very nearly mentioned in comment #9, but not quite: orbital datacentres. Lots of free solar power, and you could potentially even manufacture the chips in orbit.
There would be some transmission lag because of lightspeed limitations, so you would probably use it for big number-crunching primarily.
Originally shared by Winchell Chung
Charles Stross Trigger Warning
Speculations of other uses for the monstrous payload capacity of SpaceX’s proposed booster.
http://www.antipope.org/charlie/blog-static/2016/09/what-else-can-you-do-with-a-bi.html
Cooling can be an issue. Facilities and cooling equipment cost as much or more than servers, in our supercomputer systems.
I imagine, too, that the cooling issues would be rather different in space. Especially if you didn’t pressurise the facility.
There has to be something published about some these probes sent to Venus and Mercury, concerning cooling of their systems. Hmm…