Minecraft during its early phases, since it was created with Java, had a web version readily available. Recently as the project has grown this in browser version has been removed, and Minecraft can only be played via download. In a ThreeJS example, it was shown that it is possible to create a Minecraft version through HTML5 for in browser.
While the example is very rudimentary, it works as a very good proof of concept. The controls are simple as you fly around and can see what has spawned and there is no collision with the blocks. If you want to see the example for yourself click here.