E.T. the Extra-Terrestrial
E.T the Extra-Terrestrial was one of a few games on the Atari 2600 that actually had a story\ending (Most games just went on an infinite loop and just ended when it went to fast for a player to handle). As it has an ending, a speed run is possible.
http://www.youtube.com/watch?v=N-Ixt92qIBM - 1 minute 1 second
This Run was only partially tool assisted to the point that the game was saved so that the player knew where all the pieces of phone were and the landing and calling site were before the run. The actual character was still controlled by a human rather than a machine.
http://www.youtube.com/watch?v=TyqU8FPTO-U - 1 minute 21 seconds