I think an application configuration is an excellent use of the Singleton pattern. I tend to use it myself to prevent having to reread the configuration each time I want to access it and because I like to have the configuration be strongly typed (i.e, not have to convert non-string values each time). I usually build in some backdoor methods to my Singleton to support testability — i.e., the ability to inject an XML configuration so I can set it in my test and the ability to destroy the Singleton so that it gets recreated when needed. Typically these are private methods that I access via reflection so that they are hidden from the public interface.
EDIT We live and learn. While I think application configuration is one of the few places to use a Singleton, I don’t do this any more. Typically, now, I will create an interface and a standard class implementation using static, Lazy<T> backing fields for the configuration properties. This allows me to have the “initialize once” behavior for each property with a better design for testability.