While not commercially incredible successful as a single release per se, Alphaville's 1984 poignant anthem "Forever Young" became an instant cult classic, notable for having been covered many times, included on many TV shows, movies, and commercials, and playing probably as the final, teary-eyed song at most proms and other teenaged dances during much of the 80s (I know they did at mine, and I didn't graduate high school until 1990!)
Notably, less than a year after it's release, Laura Branigan covered it, and sang it as part of her encore at every concert until her untimely death in 2004 (I'll probably eventually include some Laura Branigan here as well… although I might give this one a pass, since I tend to avoid covers except in exceptional circumstances.)
It's a cult classic for a reason. Give it a listen if you haven't heard it in a long time, and you'll see what I mean; this is one of the most beautiful and emotional pop songs in my collection. Alphaville's debut album is actually full of all kinds of undiscovered gems, and while they wandered "astray" for many years experimenting with different sounds, their 1997 "back to roots" CD Salvation is a fun one too.