A mod of Minecraft Alpha 1.2.6 complete with SinglePlayerCommands, fixed authentication (register for free now!), and more.
It doesn't require the Minecraft Launcher or a Minecraft account (though a launcher is provided to keep the game up to date), and can be started just by running the JAR file.
Please note that it is a work-in-progress, so expect crashes. It's currently pretty stable though.
Minecraft is a game about placing blocks to build anything you can imagine.
At night monsters come out, make sure to build a shelter before that happens.
It also has music by C418!