TAS: Super Mario Bros. 3 "Game-End Glitch" in 2:54.98 by Lord Tom and Tompa
This TAS uses a "Wrong Warp" to rescue the Princess in record time without beating Bowser or even getting to World 8!
Taking a pipe in the wrong direction takes Mario to an invalid area of the map, resulting in a glitch where the CPU tries to read instructions from data representing (among other things) the x positions of enemies.
Carefully positioning 3 enemies (one piranha plant and 2 koopa shells) manipulates the CPU to read an instruction that jumps to the ending.
See http://tasvideos.org/4288S.html for more details on how this was done.
Thanks to RAT926 who discovered the wrong-warp, and HHS who figured out the technical details.
For more about tool-assisted movies in general see tasvideos.org.