If you check this blog semi-regularly, you may remember my post from just a couple of weeks ago. Sure enough, just during the past week I received notice of this and this.
When I was in college - back in the Dark Ages of the 1980s - I remember the first "homemade" music video, which was a novelty at the time. It was a Make Your Own Video contest for Madonna's "True Blue." The winning entry, if memory serves, was produced by a couple who spent a few thousand dollars on professional resources.
About ten years later, the band Bon Jovi gave dozens of audience members Super 8 movie cameras and told them to just shoot whatever they wanted during a show. The film was turned in at the end of the concert, and the resulting footage was edited into a video ("Bad Medicine", IIRC). Interestingly, but not surprisingly, the professionally-edited Bon Jovi video was all over MTV. I think I might've seen the Madonna one a couple of times after the initial winner reveal, but that's all.
I'm sure there will be more - if you come across any, please send them to me. We're disqualified from a lot of these competitions because we're professionals, but I get a kick out of seeing the submissions.