When asked who does the best job of managing their Facebook page and community, I recommend looking at two pages:- for e-commerce: ShoeDazzle (and yes, it's a Polaris company) - for media and big brand: the NBA The NBA does a fantastic job of updating the page daily and engaging fans with questions, polls, and timely / unique content (such as the "5 Best Plays of the Day").
Here is a good, simple example that takes advantage of the NBA's Facebook community and their daily interactions: the NBA updates its Facebook profile picture to reflect that day's televised games. They do this each and every day. In fact, if you visit the NBA's profile picture page, you can scroll endlessly through previous profile pictures.