When should an object (i.e. an application-wide properties file) be kept in the session, as opposed to creating a singleton to keep it? When should each of these approaches be used?
Note: I am working on a clustered environment, if that makes any difference.
If it's supposed to be application-wide, then you should not store it in the session scope, but in the application scope. With storing in the session scope, you're unnecessarily duplicating the same data for every visitor. A singleton is also not needed at all, just instantiate once during server startup with help of a ServletContextListener and store it in the application scope using ServletContext#setAttribute().
+1 to BalusC, but I suspect that was just a typo on your part.
As for singletons, it depends on what you mean by singleton. If you have an EJB annotated with @Singleton, then that's fine (other dependency-injection providers may also support this pattern).
If you're talking about the standard singleton pattern, where you keep the instance in a static variable, then that's a bad idea. You should generally avoid static variables in Java EE or servlet containers, because the class loading can be a bit tricky - you may wind up with multiple copies when you don't expect it, or you may be sharing a single copy between different applications, or you may be keeping stuff in memory when you redeploy your application. You can make an exception in cases where the variable isn't exposed outside the class, and you don't really care how many copies of it you have (for example, logger objects).
Note: I am working on a clustered environment, if that makes any difference.
I don't disagree with what Mike and BalusC have already written, but I feel you're entering territory where implementation details matter. What you do and how you do it will depend on the back-end services, what sort of clustering, and what the application requirements are. I think the question is too broad to give specific answers.
All Java EE profiles share a set of common features, such as naming and resource injection, packaging rules, security requirements, etc. This guarantees a degree of uniformity across all products, and indirectly applications, that fall under the “Java EE platform” umbrella. This also ensures that developers who are familiar with a certain profile, or with the full platform, can move easily to other profiles, avoiding excessive compartmentalization of skills and experience.
JEE specifications define a certain level of compliance but the goal isn't to make every infrastructure heterogeneous. This sort of thing adds complexity to an already nebulous problem domain.