This week's book giveaway is in the OO, Patterns, UML and Refactoring forum. We're giving away four copies of Refactoring for Software Design Smells: Managing Technical Debt and have Girish Suryanarayana, Ganesh Samarthyam & Tushar Sharma on-line! See this thread for details.
I actually started a discussion of this here once in the past, and these kind folks enlightened me. Now I feel pretty good about saying "That's what we're doing!"
Scrum is older than XP, and influenced XP's design. The two are really quite compatible. XP is a superset of Scrum, as it addresses many things that Scrum doesn't. The major change, as I see it, between Scrum and the XP Planning Game is that in Scrum the developers have more of a direct hand in choosing what stories go into each iteration based on customer input, whereas in XP the choice is made by the customer based on developer input.
My personal experience (two projects, now) is that XP planning can naturally become Scrum in a situation where you've got multiple "Goal Donors", a detached "Gold Owner", and a fairly broad project charter. Every three weeks you peel three weeks worth of work off the top of the large backlog of tasks. It's not a bad way to work if the software's target audience is a large group of expert users, many of whom are providing stories.
The only drawback is that if the Gold Owner does swoop down on you once in a while, it can be extra hard to make long-range milestone projections. XP forces you to keep at least a straw-man long-range plan, while Scrum doesn't.