<p>How is it possible to read/write to the Windows registry using Java?</p>

Yes, using the java.util.Preferences API, since the Windows implementation of it uses the Registry as a backend.
In the end it depends on what you're wanting to do: storing preferences for your app is what the Preferences does just great. If you're wanting to actually change registry keys not having to do with your app, you'll need some JNI app, as described by Mark (shameless steal here):
From a quick google:
Check the WinPack for JNIWrapper. It has full Windows Registry access support including Reading and Writing.
The WinPack Demo has Registry Viewer implemented as an example.
Check at
http://www.teamdev.com/jniwrapper/winpack/#registry_access
And...
There is also try JNIRegistry @
http://www.trustice.com/java/jnireg/
There is also the option of invoking an external app, which is responsible for reading / writing the registry.