Mario Teaches Typing
While hardly the best typing game available, just being associated with Mario makes this the most recognizable of the typing challengers. Like the slightly-more adult Typing of the Dead, the game is all about typing - and typing as fast as possible. Mario is controlled by typing instead of your controller.
The levels are setup to resemble stages in Super Mario Bros.. There are enemies to hop on, blocks to jump into, and Princesses to save - you'll just have to type to make progress. Letters, and eventually words or phrases impede your progress in the standard typing-game format. Look, I couldn't turn down Mario as a child, so Mario Teaches Typing earned most of my typing-game time by default.
Also, that terrifying rubbery Mario CGI face was born in Mario Teaches Typing.