I use static generic classes for caching reflection-heavy code.
Let’s say I need to build an expression tree that instantiates objects. I build it once in the static constructor of the class, compile it to a lambda expression, then cache it in a member of the static class. I often don’t make these classes publicly assessable – they are usually helpers for other classes. By caching my expressions in this way, I avoid the need to cache my expressions in some sort of Dictionary<Type, delegate>.
There is an example of this pattern in the BCL. The (DataRow) extension methods Field<T>() and SetField<T>() use the (private) static generic class System.Data.DataRowExtensions+UnboxT<T>. Check it out with Reflector.