Delegates are extremely useful when wanting to declare a block of code that you want to pass around. For example when using a generic retry mechanism.

Pseudo:

function Retry(Delegate func, int numberOfTimes)
    try
    {
       func.Invoke();
    }
    catch { if(numberOfTimes blabla) func.Invoke(); etc. etc. }
    

Or when you want to do late evaluation of code blocks, like a function where you have some Transform action, and want to have a BeforeTransform and an AfterTransform action that you can evaluate within your Transform function, without having to know whether the BeginTransform is filled, or what it has to transform.

And of course when creating event handlers. You don't want to evaluate the code now, but only when needed, so you register a delegate that can be invoked when the event occurs.