Obviously in the United States, the music video was spectacularly thrust into prominence in the early 1980's (1981 IIRC) with the inaugural episode of Music Television (Now MTV), which originally featured nothing but music videos.
The original video for this was The Buggles, "Video Killed the Radio Star", however there had been other music videos for years before that. Tony Bennett claimed to have invented the music video in the mid 50's about the same time that Elvis Presley filmed the video for Jailhouse Rock.
Before and after this, there had also been television shows (such as BBC's wonderful "Old Grey Whistle Test" that featured mostly unknown bands) that were mostly live performances, but also had occasional clips of music. There were also short releases of film clips from musicals as stand alone items. (Madonna's Material Girl video was a pretty good copy of the title song from Monroe "Diamonds are a Girl's Best Friend").
What is the first occurrence of the "music video" in any form, and how did it grow into the ubiquitous mini film that we are familiar with now?