From the technical standpoint, other answers have addressed the differences.
From a semantics perspective, events are actions raised by an object when certain conditions are met. For example, my Stock class has a property called Limit, and it raises an event when the stock prices reaches the Limit. This notification is done via an event. Whether anyone actually cares about this event and subscribes to it is beyond the concern of the owner class.
A delegate is a more generic term to describe a construct similar to a pointer in C/C++ terms. All delegates in .Net are multicast delegates. From a semantics perspective, they are generally used as a kind of input. In particular, they are a perfect way to implement the Strategy Pattern. For example, if I want to sort a List of objects, I can provide a Comparator strategy to the method to tell the implementation how to compare two objects.
I have used the two methods in production code. Tons of my data objects notify when certain properties are met. Most basic example, whenever a property changes, a PropertyChanged event is raised (see INotifyPropertyChanged interface). I have used delegates in code to provide different strategies of turning certain objects into string. This particular example was a glorified ToString() list of implementations for a particular object type to display it to users.