Something horrible happens on a mining spaceship:
Alien
Dead Space
If you broaden this from just 'mining ship' to include "in deep space where no-one can escape".. you'd end up with a MUCH bigger list (though I remember seeing a bunch, I can't remember the titles, other than):
2001
Event Horizon
Ghosts of Mars (which actually, like Alien, I think is more a horror movie set in space, rather than SciFi) [and had one of only a very few soundtracks that I've ever bought: the opening tune kicks ass, and Buckethead tunes are most always great!]
Lost In Space [which wasn't so much SciFi, or horror, but was just really, really sad

]
And, of course, if you broaden this to "anyplace where people can't escape" you end up with a large part of the genre.

Like (just a few)...
The Abyss
Sphere
The Thing