Listen.
Angry customers want to be listened to and taken seriously, more than anything.
Barry Moltz wrote an excellent book about customer service and dealing with angry customers, and in it he suggests not just assuming the "customer is always right" because that may not be true.
Instead, listening and taking the customer's anger seriously and dealing with it is the best course. Customers want to know they are being heard.
The book is called
BAM: Delivering Customer Service in a Self-Service World.