Despite the fact that there is not an EarthBound related game on the Nintendo 64 console, Ness does make an apperance in Super Smash Bros. Ness is one of the four secret characters in Super Smash Bros. and is the toughest of those four to get.

How do I unlock Ness?
In order to unlock Ness you must play through the single player game mode and beat it on the "Medium" difficulty setting with only three lives and without using a continue. This is a duanting task to complete for a beginner, but really is not that hard at all once one becomes comfortable with the game.