Sometimes the simplest things are the best. With games that is no different and with Minecraft I've been playing with blocks. Now there is an online Alpha version at the main site and a first draft version here.
The alpha (main link) is a multiplayer version and has things like saving builds. The first draft is just a single player with no saving. It's been fun to mess around with since I'm waiting till the product is more finalized before deciding to buy.
The basic thing to do in the single player game is build things and explore. So far I've built three houses and have done some serious cave diving in to the earth to the point where I found lava. I also ended up flooding one cave with the water I captured for my swimming pool from the ocean.
NOTE: You will need Java installed to run the game in your web browser.