Muse's music video for "Sing For Absolution" features a spaceflight to retrieve a massive capsule containing thousands of cryogenically frozen people and take them to Earth. Problem is, when they get there, Earth is an unrecognisable, let alone uninhabitable wasteland akin to the surface of Mars, and it looks like it has been that way for some time. The only things that let the viewer know it is Earth are Big Ben and what remains of a bridge.
Masaki Yamada's EZO song Fire Fire is the world after a nuclear holocaust.
The last verse of "99 Red Balloons" describes the city the song took place in, only after the nuclear holocaust, from the viewpoint of the girl remembering what had happened.
The Postal Service song "We Will Become Silhouettes" seems to be set in the aftermath of nuclear destruction. The titular silhouettes are a reference to the ghostly images of people that were left behind on walls after the nuclear bomb drops on Hiroshima and Nagasaki◊. In a classic example of Lyrical Dissonance, the song sounds like a normal peppy, Postal Service electro-pop love song.
Black Sabbath's song "Electric Funeral" from "Paranoid" portrays a struggle for survival on a post-nuclear Earth.
Edge Of Sanity's song "Crimson" takes place in a post-apocalyptic Earth where humans can no longer breed.
Electric Wizard has a song called "The Sun has Turned to Black" which describes the very end of humanity by unknown means.
Running Wild's song "Straight to Hell" is about bunch of survivors trying survive in post-apocalyptic world and "Land of Ice" is about Time Travel to a future where the world is caught on nuclear winter.
Moby said his "South Side" song is about a post-apoc world:
Here we are now going to the south side I pick up my friends and we hope we won't die Ride at night, ride through heaven and hell Come back and feel so well
I Nomadi and Francesco Guccini, "Noi non ci saremo" ("We won't be there"), spends only the first verse on the presumably thermonuclear extinction of mankind; the rest of the song is bleakly optimistic (life recovers, and Earth will be better without us). A far cry from the juvenile destruction porn of some heavy metal bands.
Jimi Hendrix's "1983...A Merman I Should Turn To Be" has the protagonist and his lover turn into mermaids and dive to the bottom of the ocean to escape a nuclear holocaust.
Klaus Nomi's music follows a plot: "Total Eclipse" warns of nuclear annihilation, and the aptly titled "After the Fall" is this.
Hawkwind: "Who's Gonna Win the War" and "Damnation Alley" (the latter based on the Roger Zelazny novel).
Michael Moorcock's album The New World's Fair (featuring members of Hawkwind) seems to be based on this trope. Its cover depicts a funfair in the distance with a "Danger - Radiation" sign in the foreground.
Then there's Hawkwind soundalikes Underground Zero, whose song "Atomchild" seems to be set in a post-apocalyptic future (though it's really hard to make out the words and there's no lyric sheet).
The Talking Heads song "(Nothing But) Flowers" takes place years after humanity has given up technology and now lives as hunter-gatherers while the surrounding architecture rots away. The singer becomes increasingly irritated by the lack of modern conveniences and reminisces about life before the end.
"Come Away Melinda", perhaps this trope's most understated yet touching example.
Porcupine Tree's "A Smart Kid" is an incredibly depressing song set after the end, stated to have been some sort of war.
German heavy metal group Rage have a song named "Take me to the Water", which deals with a lone survivor in an already dried-out Earth looking for a mythical source of water.
Gotye's music video for Eyes Wide Open shows a band of strange, thin limbed creatures wandering Earth, starting with the aftermath of a nuclear war and going back in time to the beginning of life on Earth.
"Wooden Ships" (written by Jefferson Airplane guitarist and SF Fan Paul Kanter, in collaboration with members of Crosby, Stills and Nash, and a hit for both groups) depicts ocean-dwelling survivors of an unspecified apocalyptic event.
This forms setting for Lindsey Stirling and Pentatonix's collaborative cover of "Radioactive". The video is filmed around some old graffitied buildings and junk in the middle of a desert, and the desolate feeling is enhanced by the heightened contrast in the video.
The Imagine Dragons song "Radioactive" alludes to a nuclear apocalypse. The music video for "It's Time" shows the band traversing a desolate wasteland (which somewhat resembles San Francisco).