Those that make these videos say law is a little bit fuzzy. Although the songs are copyright, the videos could be considered parody (according to law, a parody is legally considered an original work), in which case it is considered "fair use" to make and distribute the video. I personally have trouble with that being the case since original material is being used, but the courts haven't decided yet.
From what I see of his work, it isn't just little clips, but most of the song, plus there is copyrighted images & video. Probably not something that can be considered parody.
