What does it take for a game to be fully accessible?

For different types of games, it means that various features are provided to make the game possible for all levels, and to provide the minimum of repetition (having to play the same part of the game over and over again).

First-Person/Third-Person Shooters:
-Have a manual save system that allows the player to save at any point.  Barring this, have sufficient checkpoint saves that a gamer should have to spend no more than 60 seconds retracing his steps.
-Have varying difficulty levels, including an Easy level which anyone, including those without any FPS experience, can progress through the entire campaign.
-Do not have any enemies that can perform one-hit kills, especially if your checkpoint system sucks (I’m looking at you, Kane & Lynch!)

Real-Time/Turn-Based Strategy Games:
-Have varying difficulty levels, including an Easy level where anyone, regardless of experience playing RTS games, can complete all aspects of the single-player campaign.
-Have a save system that can save during a mission, and not just at the end of it, so that players are not forced to play a potentially hours-long mission at one sitting.

Sim Games (Sim City/Spore/etc.):
-Have a “sandbox” mode where a player can play around with all features of the game, with unlimited funds/resources.
-Allow a player to use the sandbox to build any type of thing in the game, don’t restrict certain types of content that can only be unlockable after meeting a certain challenge.
-Allow saving at any time.

Free-roaming games (a la GTA):
-Allow full access to the entire game world.  Do not lock away parts of the environment until a player has finished completing certain missions.
-Allow saving at any time, in any location, even if a mission is currently in progress.

Platform games (Mario, Sonic, etc.):
-Save the game after each completed act or level – do not force the player to successfully complete multiple segments of the game before they are allowed to save.
-Have sufficient checkpoints within the level to prevent a player from having to retrace considerable amounts of the level after failing to complete a single difficult jump or obstacle.
-Especially do not have a game situation where there are no save points at all – this is fine for an arcade which is trying to collect as many quarters as possible, but should not be acceptable for a game intended for personal use.