<p>I'm in the process of weeding out all hardcoded values in a Java library and was wondering what framework would be the best (in terms of zero- or close-to-zero configuration) to handle run-time configuration? I would prefer XML-based configuration files, but it's not essential. </p>

<p>Please do only reply if you have practical experience with a framework. I'm not looking for examples, but experience...</p>

If your hardcoded values are just simple key-value pairs, you should look at
java.util.Properties
.  It's a lot simpler than xml, easier to use, and mind-numbingly trivial to implement.
If you are working with Java and the data you are storing or retrieving from disk is modeled as a key value pair (which it sounds like it is in your case), then I really can't imagine a better solution.
I have used properties files for simple configuration of small packages in a bigger project, and as a more global configuration for a whole project, and I have never had problems with it.
Of course this has the huge benefit of not requiring any 3rd party libraries to utilize.