The run the gambit from the mundane such as hurricanes, tornadoes and volcanoes to the more esoteric such as meteors and global events. You can get away with a simple adventure plot for stories that don't have an impact on a large area. Think of movies like Twister. Tornadoes only effect a small population, so you can concentrate more on the characters.
Volcanoes and hurricanes are more mid level. They effect a large population, so you need to make sure and incorporate all sides of the conflict from city officials to the people on the street. Global disasters can be difficult to write because it involves everyone. You can't have a planet killer coming to Earth and not say that only the U.S. is going to something about it.
Mid and large scale disasters require several separate frames of reference. You need a microcosm to provide the emotion, but you need the larger picture of military and governmental oversight to give it realism. If you want to write a disaster story, then start out small. Do a lot of research on realistic reactions to the disaster and use that in your plot. While Bruce Willis and can single handed take on a giant planet killing rock for major cinematic value, that's not going to be realistic.