<p>If you had to make a case to a business about adopting or moving to an agile development methodology (like SCRUM or XP etc) what case would you make (how do you sell the concept)?  </p>

<p>e.g. 
<li>How would you describe the concepts and benefits to a non-technical person?</li>
<li>If you have successfully done so, what was the winning argument/case/rationale?</li></p>

<p>Edit: The reason I ask is that a friend of mine (he is the solution architect at a firm) is currently trying to decide how to approach his management about exactly this topic, and I've given him what I can in terms of suggestions.  Curious especially to hear from those who have successfully made a case to move to an agile-aligned methdology. </p>

Non-technical people are interested in projects done on time and within budget with good quality and which would satisfy their requirements at the time of the delivery. You should focus on how Agile helps to deliver those qualities.
It's sometimes quite difficult to sell Agile to a non-technical person for two reasons:
The concept of not trying to plan 100% ahead is not really intuitive
Quite a lot of people claim that they use Agile, fail miserably to deliver anything and give the great SDP a bad name
Talk about Agile process ability to handle changes.
It's usually easier if you work with the customer who already work with you. You could easily show them for example all of the change requests accumulated over the time and show how they affected the schedule and the costs of the project. You could then go into explaining how Agile process will help handling such cases.
Along the same line you could take the initial estimations done on a 'waterfall project' and compare them with real-life results.
I would also talk about the Agile approach to quality. Testing during iterations increase the quality considerably. Short iterations with immediate feedback are great help too, mention them.