I know I can take screenshots with java.awt.Robot and with Windows, but can I take movies of the screen? Is there some software out there that can do that?
Crossposting sucks… and well yes, I know 2 programms wich can do that kind of stuff 
Nyah 
No crossposting…
You should take a look at Hypersnap DX…
Chman
If you are looking for a Java solution, I think it’s possible to use Java Media Framework for this. Check out the screen grabber example at http://java.sun.com/products/java-media/jmf/2.1.1/solutions/ScreenGrabber.html. It says it can even stream captures over the internet. 8)