Customers and other species

 This question was recently posted by Philip Smith of Blueberry Quill in a LinkedIn forum. It was prompted by Colin Shaw's recent article on the subject. Referring to it, Philip asked:

In recent days Gary Lemke of CRMAdvocate.com fame sparkled renewed interest in the 'United Breaks Guitar' story (also known as the Guitar Man story in 'professional' social media and customer strategy circles.

 This was my answer to a question posted on Quora, but I shamelessly reproduce it here because I think the challenge is important and would welcome your opinions:

Q: Should employees break the rules to help customers? 

(Context: "We all love the shop assistant or call centre employee who goes the extra mile tohelp us. But when these employees' actions use their organisation's resources or break its rules, do they benefit or damage the organisation?")

We hear a lot about Customer Engagement nowadays: everyone seems to know about it, many say they are 'doing it'. I would challenge the happy practitioners and the self-proclaimed gurus to come up with a consensus definition, though. What is Customer Engagement?