Embedded scripting languages work well for storing configuration information as well. Last I checked, the Mozilla family all use JavaScript for their config information.
Next up, they are great for developing plugins. You can create a custom API to expose to the plugin developers, and the plugin developers gain a lot of freedom from having an entire language to work with.
Another is when flat files aren't expressive enough. If you want to write data driven apps where behavior is parameterized, you'll get really tired of long strings of conditionals testing for config combinations. When this happens, you're better off writing the rules AND their evaluation into your config.
This topic gets some coverage in the book Pragramtic Programmer.