Ahh, yes, Axel F: the song that everyone remembers, by Harold Faltermeyer, the name that nobody remembers. First appearing in 1984 on the Beverly Hills Cop soundtrack, this wholly sythesized song is likely one of the most recognisable songs from the modern era, and is usually near the top of any list of songs people compile when striving to embody the 1980s.
Axel F, presumably named for Eddie Murphy's character "Axel Foley" in the aforementioned film, is one of a series of notable musical numbers that Faltermeyer wrote for movies, alongside the Top Gun theme and most of the soundtrack for The Running Man. Thus, after these successes, it's no wonder that in 1988, Faltermeyer finally came out with his first album, titled Harold F. Though the album appears to have been a commercial failure, Axel F was included as a bonus track on the CD version of this album.
These days, Axel F can be found on any number of compilation albums, generally those that focus on synthesizer tracks or on 80s music; recently, in a nod to the original, electronica artist Murphy Brown remixed a track entitled "Axel F 2003".
At one point "Axel F" was said by some to have been the first song performed completely on a synthesizer to break into the Billboard Top 40, but I have, as of yet, been unable to confirm this. Assistance in confirmation, one way or another, would be appreciated.
Some assistance with this writeup provided during (mostly futile) research at Allmusic.com