The Ann Arbor District Library has launched a summer reading game for 2011. It's brilliant.
Once you have signed up, you can get points for doing a whole set of library-related activities. Checking out books, reading them, reviewing or rating them, and adding them to published lists all give you credit. There's also points to be scored for visiting library branches, attending events, and reading and commenting on the web site.
Essentially, almost any measure that the library might be able to count and use in national surveys of library use - here's a sample set of survey data from IMLS - have some game-related scoring attached. As points accumulate, they can be traded in for gifts that are funded by the friends group. Nothing is worth very much, so the competitive aspect stays in the realm of gameplay and doesn't go off into Bitcoin-style real money that would prompt you to set up a bot army to review books for you.
I can imagine any organization that's measured by external metrics using an internal gaming system to trigger behavior that shows up when overall counts are done at the end of some accounting period. AADL had to cope with some of the point structures being not quite correct - for instance, the number of points you got for making reviews was reduced ("nerfed") because the incentive was too good.
Libraries make excellent systems to add this to because in a typical system there's so much unexplored inventory of books that there would be no worry about too many reviews. I recall a similar gameplay within Epinions more than a decade ago that somehow prompted me to write 46 reviews, including this 1999 review of their incentive system - which was a moderately lucrative game in dot-com era dollars.