Are there any reasons to use private properties in C#?

Question

I just realized that the C# property construct can also be used with a private access modifier:

private string Password { get; set; }

Although this is technically interesting, I can't imagine when I would use it since a private field involves even less ceremony:

private string _password;

and I can't imagine when I would ever need to be able to internally get but not set or set but not get a private field:

private string Password { get; }

or

private string Password { set; }

but perhaps there is a use case with nested / inherited classes or perhaps where a get/set might contain logic instead of just giving back the value of the property, although I would tend to keep properties strictly simple and let explicit methods do any logic, e.g. GetEncodedPassword().

Does anyone use private properties in C# for any reason or is it just one of those technically-possible-yet-rarely-used-in-actual-code constructs?

Addendum

Nice answers, reading through them I culled these uses for private properties:

• when private fields need to be lazily loaded
• when private fields need extra logic or are calculated values
• since private fields can be difficult to debug
• in order to "present a contract to yourself"
• to internally convert/simplify an exposed property as part of serialization
• wrapping global variables to be used inside your class

Answer 1

I use them if I need to cache a value and want to lazy load it.

private string _password;
private string Password
{
    get
    {
        if (_password == null)
        {
            _password = CallExpensiveOperation();
        }

        return _password;
    }
}