When Nintendo released the Wii, they were onto something with the reduction of buttons and change in design of the controller. The original NES controller also had very few buttons and this made it easy to learn controls. Something we must remember is that back then, there weren't any tutorials. Instead, the first level was where we experimented with the controls and then just started playing. I consider this important as this was how accessibility was defined, but we've lost that in modern gaming.
Today's AAA games tend to be complicated with hours of gameplay or text devoted to explaining how to play. This actually hurts the game's value as those who quickly understand the controls don't want to sit through long tutorials. I know that every time I picked up a new Mega Man Battle Network game, I was annoyed by the tutorial stages that just seemed to go on forever. These levels are nice for new players, but they frustrate veterans and kill the reply value of the game. This actually brings about the ironic situation where the game may be accessible to newcomers, but not accessible to experts.
On the flip side, if there is no explanation for a complicated game, then the developers risk isolating any new players. The solution is a proper balance. If the game is simple enough in gameplay, then no tutorials are needed. A good example is Super Mario Bros. where you move or jump. World 1-1 gave newcomers perfect environment to learn how to play the game while also not being annoying for experts to play. In fact, there are so many secrets in that level, experts would replay just to find them.
Now what about complicated games? Fire Emblem: Awakening did a good job here as well. Instead of a time consuming tutorial, the player was given screens of text with picture examples with the option to skip and view later. This means new players can read the tutorials whenever they want to, making it a prime example of accessibility while not impeding those who already know the gameplay.
Accessibility has a bad connotation in gaming to mean adding tutorials. However, it really means just making it so more people can enjoy and easily understand the game. It's a good goal, but it must be important to realize that it affects not only the novices, but also the experts. When that balance is achieved, the game is allowed to achieve greatness.