Super Mario Bros 3 is a very famous game for the NES. There are normally two main ways to beat it: the quick way using warp whistles to skip worlds, and the longer way which goes through all the worlds.
This run improves on the previous movie by 10469 frames (that's 2:54.18) via exploiting a bug in which very rapid input overwhelms the game's controller read routines, allowing the game to be completed directly from anywhere (in this case, the title screen). See the authors' comments for more details.
Watch this run on a real NES.