Listening for input without focus in Java
There is a library that does the hard work for you: https://github.com/kwhat/jnativehook
This is not a trivial problem and Java doesn't give you a way to do it elegantly. You can use a solution like banjollity suggested but even that won't work all the time if your errant mouse clicks open another fullsized window currently open in your taskbar for example.
The fact is, Java by default gives developers very little control over the OS. This is due to 2 main reasons: security (as citied by java documentation) and the fact that different operating systems handle events completely differently and making one unified model to represent all of these would probably not make a whole lot of sense.
So to answer your question, I imagine what you want is some kind of behaviour for your program where it listens for keypresses globally, not just in your application. Something like this will require that you access the functionality offered by your OS of choice, and to access it in Java you are going to need to do it through a Java Native Interface (JNI) layer.
So what you want to do is:
Implement a program in C that will listen for global keypresses on your OS, if this OS is Windows than look for documentation on windows hooks which is well docuemented by Microsoft and MSDN on the web and other places. If your OS is Linux or Mac OS X then you will need to listen for global keypresses using the X11 development libraries. This can be done on an ubunutu linux distro according to a Howto that I wrote at http://ubuntuforums.org/showthread.php?t=864566
Hook up your C code to your Java code through JNI. This step is actually the easier step. Follow the procedure that I use in my tutorial at http://ubuntuforums.org/showthread.php?t=864566 under both windows and linux as the procedure for hooking up your C code to your Java code will be identical on both OSes.
The important thing to remember is that its much easier to get your JNI code working if you first code and debug your C/C++ code and make sure that it is working. Then integrating it with Java is easy.