Two games a re built into the Kindle (version 3).
For Minesweeper press press Alt + Shift + M.
From there, you can use the little 5-way joystick button to navigate around. Pressing on the joystick will uncover a square, and hit M to mark a block that you think is a mine.
Once you've access Minesweeper, you can then press 'G' to access another game: GoMoku. This is just like 5-in-aRow. To go back to Minesweeper from GoMuko, just press 'M'.