In Super Mario 64 this was different: pressing "up" on the controller didn't let Mario walk forward from his own perspective; rather, it made him walk in the direction the camera was currently facing. Basically every third-person game today now uses the Mario 64 control scheme.
It is interesting that another game which had a similarly huge influence on character controls was also a Mario game: Super Mario Bros for the NES. It introduced character acceleration, dynamic jump length based on character speed, dynamic jump-height based on how long the jump button is held, and character steering in the air. Basically every 2D platformer uses this control scheme to this day. Games before that had fixed jump arcs and fixed running speed.