My cats will do all kinds of stuff - not random stuff, but stuff I actually trained them to do.
They can both use the toilet, Cinnamon can say meow on command, they can climb ladders, and one I didn't teach them (which would qualify as random) is that Cinnamon can get ice from the fridge.
Here are some videos:
http://www.bodydot.com/gallery-10902...nd-Ginger.html