Java 6 has been available for a while on Mac OS X, but if you don't specifically tell the OS to use this version, it still uses Java 5 32 bit. You can change this by dragging Java 6 to the top of the list in Java Preferences. After that, all applications started from the terminal or spotlight will use Java 6. I had a problem when using Java 6, or any 64 bit JVM. I couldn't type in any input field. Clicking around worked, but no input. Even jconsole wouldn't allow me to enter anything.
Since I wasn't very fond of the US keyboard layouts provided with the OS, I've been using the US International layout from Rainer Brockerhoff for quite some time now. Apparently, version 1.1 does not allow any input when using it on a 64 bit JVM. Downloading the latest version (which is 1.2 at the time of this writing) solves this problem.
Now everything is working as it should.
It took me a whole day to find this solution and Google didn't help. So I hope, this post will someday help someone.