Play the same saved world around the (real) world seamlessly
Solution 1:
I can't test it right now (At work) but I believe Minecraft stores its configuration data (and world data) in "$HOME/.minecraft".
If you replace that directory with a symlink to a folder in the Ubuntu One folder it should use that new folder to store it's data, if you do the same at a different computer the game shouldn't know the difference.
Solution 2:
Create a symbolic link to the Ubuntu One folder, using:
ln -s /path/to/ubuntu/one /path/to/minecraft/folder
Then make sure you sync properly and then it should work.