When lining the cookie sheets with parchment paper, is this meant more for recipes that call for greased cookie sheets or for recipes that call for ungreased cookie sheets?

I use it for everything. There are a couple of cookies that require sugar to carmelize (palmiers for one). Even that will work on parchment, it just takes a bit more patience.

I use it for all cookies as welll.............I don't grease the parchment or anything......my cookies never stick.....I also use it for messy things for dinner like bbq ribs or chicken....nothing sticks.