I am fairly sure I know of a PDF that requires acrobat (reader). The free software I have tried (mostly xpdf derivatives) only dispalays page 1 of the PDF specification (which in is PDF) format. If you want to page pages 2 to 300+ you need acrobat.
I have also experienced one PDF document which xpdf displayed fine but printed a set of black boxes. Using adobe's software worked without any problems. Explanations are welcome on the back of a post card.
Electronic journal articles, which are almost always in PDF format, are particularly prone to problems. I suspect some of them are not valid PDF but acrobat reader somehow copes with the problems, possibly by ignoring the incorrect data.
(Given the choice I prefer a 64 bit version of xpdf to acroread, partly because the former is a lot faster and shares more memory with other programs.)