I've successfully installed Minecraft under Ubuntu, but my provlem is that upon launch, all I get is a black screen.
Solution
Configure Java (Minecraft isn't compatible with version 7- switch to version 6):
Open a terminal and type:
sudo update-alternatives --config java
Open Minecraft.jar (either via the command: java -jar /path_to_minecraft/minecraft.jar) or either by right-clicking on minecraft.jar > JDKjava6Runtime.
This document, titled « Minecraft /Ubuntu - Black screen on launch », is available under the Creative Commons license. Any copy, reuse, or modification of the content should be sufficiently credited to CCM (ccm.net).