The title pretty much says it all. Looking for pros/cons, and situations where it should / shouldn't be used.
It seems fairly self-evident to me. You use Align to Pixel Grid when you want pixel accurate artwork (Anything for screen). If you don't care about pixel accuracy (print work) there's no need to use the feature.
It's not really self evident and in fact, it's a cumbersome feature which got turned into a default with CS5. The Align to Pixel Grid and Pixel Preview modes require almost two different ways of working with pixels in Illustrator. Align to pixel grid tries to position things for you automagically, meanwhile Pixel Preview + Snap to Pixels, allows you to work more directly, almost like you are in Photoshop. It's really up to you to decide which works best for your purpose. If you work all day with pixel positioning and want nothing left to chance, then I would work in Pixel Preview mode and turn off Align to pixel. There's two distinct locations for the feature. One is in the advanced section of the New Document Dialog, the other is in the top right flyout menu of the Transform Palette.