This category can include films about natural disasters, pandemics, alien invasions (though most of those I'll probably list under science fiction), animal attacks, accidents such as plane crashes or ships sinking, etc. It's often (but I would say not always) a subgenre of action films. You could also call kaiju films and zombie films "disasters", but they have their own sections. For movies set in the aftermath of large-scale, society-spanning disasters, see dystopian & post-apocalyptic films.
stuff I've seen:
The Abyss
Gravity
The Poseidon Adventure
Snakes on a Plane
Volcano
War of the Worlds (2005)