[jmillikin]

This is called "automatic mario", and is very popular on Japanese social video sites like Nico Nico Douga.

One of the most impressive examples is an 11-minute medley of video game and cartoon themes: http://www.youtube.com/watch?v=Xz0PaPpmGa8

[DarkShikari]

More specifically, this is one of the Nico Nico Medleys, a series of fan-made medleys of memetically popular songs. There are quite literally thousands of arranges of each of them.