Do these petition sites actually ever do anything? All I can think when I see them is "wow what a clever data mine".

The petition site here is WhiteHouse.gov and has done quite a few things in past.

Other sites though, I have similar thoughts!

Examples please? It's an honest question; I really can't think of anything.

The white house released the recipe for their honey ale in response to a petition:

http://m.whitehouse.gov/blog/2012/09/01/ale-chief-white-hous...

Hahaha. I'm glad that one didn't require a FOIA req.