On my quest for the truth I discovered that there are actually very few “acceptable” reasons to use a Singleton.
One reason that tends to come up over and over again on the internets is that of a “logging” class (which you mentioned). In this case, a Singleton can be used instead of a single instance of a class because a logging class usually needs to be used over and over again ad nauseam by every class in a project. If every class uses this logging class, dependency injection becomes cumbersome.
Logging is a specific example of an “acceptable” Singleton because it doesn’t affect the execution of your code. Disable logging, code execution remains the same. Enable it, same same. Misko puts it in the following way in Root Cause of Singletons, “The information here flows one way: From your application into the logger. Even though loggers are global state, since no information flows from loggers into your application, loggers are acceptable.”
I’m sure there are other valid reasons as well. Alex Miller, in “Patterns I Hate“, talks of service locators and client side UI’s also being possibly “acceptable” choices.
Read more at Singleton I love you, but you’re bringing me down.