In 1983 (an all-round good year for music; I'll have to do an entire theme week around it sometime) the British band Tears for Fears had its first chart hit, "Mad World," from their album The Hurting.
"Mad World" was an ironic song about teenage angst, with morbid lyrics set to a peppy dance beat. But in 2001, film score composer Michael Andrews and vocalist Gary Jules played the teen-angsty lyrics straight on their minimalist cover for the teen-angsty cult flick Donnie Darko. Instead of the lush synth arrangement of Tears, Andrews and Jules' cover is minimalist, featuring only piano, cello, and voice.
The 2001 version accomplished what Tears for Fears had not: a #1 hit that became ubiquitous: notably it was featured in an ad for the video game Gears of War, but was also used in dozens of TV programs, including CSI and Smallville.