The disaster movie genre is pretty identifiable, but what about songs? Let’s list songs dealing with disasters, fictional or otherwise.
Flash and the Pan, “Down Among the Dead Men” (Titanic), “Atlantis Calling”
Jaime Brocket, “The Ballad of the USS Titanic”
Bee Gees, “New York Mining Disaster 1942”
Well, there’s The Wreck of the Edmund Fitzgerald, of course.
Paper Lace covered** The Night Chicago Died**
Gordon Lightfoot has the classic Wreck of the Edmund Fitzgerald
Deep Purple has Smoke on the Water
Bloodrock’s DOA is about as explicit as you’re going to find.
Nautical Disaster, The Tragically Hip.
Falling in Love, NOFX.
Harry Chapin: 30,000 Pounds of Bananas
There’s Molly Hatchet’s Flirtin’ With Disaster. Twern’t a very big one though.
I guess you could include McLean’s American Pie and Garcia’s Casey Jones in there too.
Folk music is full of disaster songs. My favorite is “Blood On The Coal” by the Folksmen. 
How about everything on The Rising by Bruce Springsteen?
Leslie Gore: It’s My Party and I’ll Cry If I Want To
It is* too * a disaster!
Nena’s 99 Luftballons ends poorly for pretty much all involved (and a whole lot of people not involved).
Patsy & Elmo(?): Grandma Got Run Over By a Reindeer
sorry
Tom Lehrer’s “We’ll All Go Together When We Go”
Al Stewart’s “Road To Moscow” and “Constantinople.”
The Revolting Cocks wrote “38” about the soccer disaster of May 29th, 1985 at the Heysel stadium in Belgium.
They also did two songs named “Union Carbide”, Bohpal and West Virginia versions naturally.
Well, “The Morning After” and “We May Never Love Like This Again” were from disaster movies (The Poseidon Adventure and The Towering Inferno respectively) and both have a sense of forboding (and hope) about them in the lyrics.
Alan Price: “Trimdon Grange Explosion” (or Martin Carthy: “Trimdon Grange Disaster”)
New Riders of the Purple Sage: “Dirty Business”
Pink Anderson: “The Titanic”
Gentle Giant: “Wreck”
Since he died just a couple weeks ago, let’s go with Eric Von Schmidt’s version of the “traditional” (AKA: not copyrighted) “Wasn’t That a Mighty Storm,” about the Galveston Flood of 1900:
*[Chorus:]
Wasn’t that a mighty storm
Wasn’t that a mighty storm in the morning, well
Wasn’t that a mighty storm That blew all the people all away
Now Galveston had a seawall to keep the water down,
But a high tide from the ocean spread the water over the town.
[Chorus]
You know the trumpets, they give warning, sayin’ “You’d better leave this place,”
Now, no one thought of leaving 'til death stared them in the face.
And the trains they all were loaded. The people all leaving town
The trestle gave way to the water and the trains they went on down
[Chorus]
Rain it was a’ falling. Thunder began to roll.
Lightning flashed like hell fire. The wind began to blow.
Death, the cruel master, when the wind began to blow
Rode in on a team of horses. I cried, “Death, won’t you let me go”.
[Chorus]
Hey, now trees fell on the island and the houses give away.
Some they strained and drowned. Some died in most every way.
And the sea began to rolling and the ships they could not stand
And I heard a captain crying, “God, please save a drowning man”.
[Chorus]
Death your hands are clammy. You got them on my knee.
You come and took my mother. Won’t you come back after me.
And the flood it took my neighbor. Took my brother too.
I thought I heard my father calling. And I watched my mother go.
[Chorus]
You know the year of 1900, that was sixteen years ago,
Death came howling on the ocean. Death calls, you got to go.
[Chorus 2x] *
Then for one which, if it were ever copyrighted, probably has a copyright still active, Memphis Minnie and Kansas Joe McCoy’s song about the Great Mississippi Flood of 1927, “When the Levee Breaks.” If you play Led Zeppelin’s version loud enough you could probably break a levee. Both songs contain lessons lost on the current residents of the Gulf Coast.
Jimmy Buffett: Volcano
Somehow I don’t feel I’ve entered into the spirit of this thing properly. 
Harry Chapin - “Dance Band on the Titanic”
There’s a gospel recording from the 40’s about “The Burning of the Winecoff Hotel,” performed by Pete Cassell among others. (The Winecoff in Atlanta was the site of a hotel fire in 1947 which killed 119.)
Dwight Yoakam - “Miner’s Prayer”:
I still grieve for my poor brother
And I still hear my dear old mother cry
When late that night they came and told her
He’d lost his life down in that Big Shoal mine.
The Grateful Dead - “Casey Jones”
And then there’s the traditional song “[The Ballad of Casey Jones](http://web4j1.lane.edu/~rogers_s/song_lyrics.htm#Casey Jones)”.
Speaking of train wrecks, there’s the traditional “Wreck of the Old '97”
“When the Levee Breaks” - Big Mama Thornton (oh, and some band called “Led Zeppelin” did a cover of it too.) This song actually predicted a disaster.
“A Hard Rain’s Gonna Fall” - Bob Dylan (not necessarily a disaster song per se, but a dire warning of forboding times to come)
“the House at Pooneil Corners” - Jefferson Airplane (nuclear war song)
“Wooden Ships” - CSN / Jefferson Airplane (aftermath of nuclear war song)
“July 6th” - John & Mary (a bit obscure one, but a song about a disastrous fire and ensuing stampede at a circus. Supposedly based on a real event.)
“New Orleans Is Sinking” - Tragically Hip (another song that anticipated disaster. The same one that Big Mama spoke about.)
“Do They Know It’s Christmas?” - Band Aid. (I think the devastating starvation that occured in Ethiopia counts as a disaster.)
“Where Were You When the World Stopped Turning?” - Alan Jackson (cynical, hateful cash-in on the WTC/pentagon disaster. But a disaster song nonetheless.)
Do man-made and petulant disasters count?
“Boom! goes London, Boom! Paree…”