Singleton is a common pattern implemented in both native libraries of .NET and Java. You will see it as such:

C#: MyClass.Instance

Java: MyClass.getInstance()

The question is: when writing APIs, is it better to expose the singleton through a property or getter, or should I hide it as much as possible?

Here are the alternatives for illustrative purposes:

Exposed(C#):

private static MyClass instance;
public static MyClass Instance
{
    get {
        if (instance == null)
            instance = new MyClass();
        return instance;
    }
}

public void PerformOperation() { ... }

Hidden (C#):

private static MyClass instance;

public static void PerformOperation()
{
    if (instance == null)
    {
        instance = new MyClass();
    }
    ...
}

EDIT: There seems to be a number of detractors of the Singleton design. Great! Please tell me why and what is the better alternative. Here is my scenario:

My whole application utilises one logger (log4net/log4j). Whenever, the program has something to log, it utilises the Logger class (e.g. Logger.Instance.Warn(...) or Logger.Instance.Error(...) etc. Should I use Logger.Warn(...) or Logger.Warn(...) instead?

If you have an alternative to singletons that addresses my concern, then please write an answer for it. Thank you :)