I'm a sucker for natural disaster movies, even the bad ones. I do prefer if the science is right, and I grudgingly accept "mostly right." Tell me an interesting story, with characters I like, too. Some of my favorites are:
Dante's Peak. While some portrayals of the eruption were wrong, and other bits were understandably changed for the movie (if you portrayed ash realistically, it'd be a movie with voices coming out of impenetrable gray stuff, which would be a waste of attractive actors), the special effects were way cool for the time--and they still hold up.
Supervolcano, BBC. A two-part show about a Yellowstone supereruption (which you shouldn't spend a second worrying about--you're far more likely to be eaten by a lion or killed by a cow in your lifetime). It has all the science right, it bothers to explain a good deal of it without slowing down the action, and it portrays officials as trying to do their best/their jobs, which I think is what would happen in a major disaster. I wish Hollywood usually did half so well with sticking to the facts as the British filmmakers did here.
The Great Los Angeles Earthquake. Another made-for-TV movie. Again, they have a lot of the science right. I dislike the one-dimensional bad guy character (played by "the Paper Chase guy," as we MSTies call him), but the time frame, what an earthquake is like, what can go wrong, and the aftermath is much like I'd expect it to be IRL. There'd be even more looting in an urban area, I suspect, but the confusion and horror, I believed. And remember, to relatives in the New Madrid Seismic Zone, that's what'd happen to a prepared city! If another big New Madrid quake happens (as it did in my novel Quake), you guys are in serious trouble.
Deep Impact. As with other Hollywood films, I force myself to be happy when they get half of the science right. Here, they probably didn't even hit 50% (by the time an asteroid was visible with a tiny backyard scope, everyone on the planet would know about it, and if you explode one, the mass isn't changed, so you're still going to get superheating of atmosphere, so li'l Frodo and his wife there would have been flash fried at the end, and American politicians don't get to decide what celestial objects are named--international scientists do, via well-established convention--and so on). But hey, I liked it anyway.
In my opinion, there hasn't been a great weather disaster movie yet. I wish someone would make one. There are plenty of real-life weather disasters to choose from.
And I'll add three human-caused disaster movies I like:
The Day After. Yet another TV movie (Made for TV movies get a bad rap--and probably deservedly so--but with disaster stories, TV seems to do better than film). Nuclear holocaust. Shocking upon first viewing, back when. Spoiler: things don't turn out very well.
Testamant. A nuclear disaster film without any explosions. Follows residents of one small town as radiation sickness takes them out one by one. Elegiac, touching, and very well acted.
Virus. (復活の日 Fukkatsu no hi) Japanese 1980 film, partly in English. Multiple disasters lead to an end-of-world scenario. Unknown/under-appreciated in the US. Find the long version, if you can.
Tell me yours! (even if it is Sharknado.)