GameLife has the full Miyamto transcript:
http://www.wired.com/gamelife/2009/10/shigeru-miyamoto/
Miyamoto's answer to the below question perfectly nails why I love Mario games:
Tom Holoien, Nintendo Power: What elements would you say a Mario game has to have whether it’s 2-D or 3-D, and for you personally, what makes a Mario game a Mario game besides the characters?
Miyamoto: So to me, what’s really important about a Mario game is that it be simple to control and easy to understand. And that when you as the player is playing the game, the physics in the game are understandable to you, so that when you hold the controller, you play it in a way that you understand what you’re supposed to do, you understand the environment, and then you begin to unleash your own gameplay creativity. You try different things. The response that you get from the environment into what you attempted to do in the world feels natural to you, and ultimately the game itself becomes kind of a back and forth between us the developers in trying to expect what types of creative things you might try to do as a player and you the player in terms of the response that you’re expecting to get in the game. And to me, a Mario game is really unleashing the player’s creativity within the world that you’ve created.