Google's new image orientation captcha is a good example of a productivity game. The core skill required is an ability to discern between an upright image and a not-upright, or incorrect, image.
Players use these core skills to work at re-orienting the images correctly.
The paper is here:
"Given a large repository of images, such as those from a web search result, we use a suite of automated orientation detectors to prune those images that can be automatically set upright easily. We then apply a social feedback mechanism to verify that the remaining images have a human-recognizable upright orientation."
Tech Blorge: http://tech.blorge.com/Structure:%20/2009/04/19/google-tries-out-picture-captchas/