2006 Addition: New Super Mario Bros has now reverted action controls back to two buttons; with some simplistic implementation of moves from the 3D games using simple d-pad presses at certain times. It also manages to cram in a dozen moves too, which is an achievement with only two buttons and a d-pad.
Sonic 2D commendably only uses one button for all actions, with intuitively designed use of the D-pad required to perform additional movements.
Coincidentally enough, the all-time best sellers do not use tutorials and the newer, more hi-tech titles do.
SMB3 perhaps assumes you’ve read the manual and introduces challenges and ideas, gradually increasing their complexity as time goes on.
Rayman does the same, as does Crash and 2D Sonic.
Jak and Daxter, Super Mario Sunshine and Sonic Adventure however, all use unavoidable tutorials at the very beginning of the game.
This clearly shows a desire has arisen in recent years to make things more accessible for prospective players.
2006 Addition: NSMB seems to grant accessibility by rewarding you almost constantly. So instead of making the game easy by the in-game obstacles, it sets up a safety buffer for lesser-skilled players by giving them regular rewards, access to power-ups and alternative routes should they get stuck. At least that’s my theory on it.