Over on the EXRX forums, Jungledoc aka Andy Bennett has brought back the Pullup Challenge.
To get more pullups than you did before. Not beating each other, but improving your own numbers.
What kind of pullups count? Any, it's your personal challenge. Want to set a new 1-rep max? Fine. Wide-grip pullups? Fine. Set a total reps record across a few sets? Fine. Get one good unassisted pullup? Awesome. For example, I'm planning to add 1 rep to my chinups (palms facing me, shoulder width grip). For you it could be something else, as long as it's some kind of pullup.
Help! How do I improve my pullups?
Fortunately a lot has been written about improving pullup numbers. Here are just a few:
Jen's New Chin Up PR
Strength Basic's Pullup posts
The Ultimate Pullup Video
That's just to get you started. Test your max, train well for a month, and see where it gets you. A new PR is just a month away!