Check out this thread on superuser, which explains how PDFs can do damage:
PDF files are both complex (so easy to have bugs in parsing code that can be used for malware) and have Javascript, which can be used for nefarious purposes as well.
A PDF exploit is one way in which these file types can be dangerous:
Earlier this month, Belgian researcher Didier Stevens demonstrated how malicious PDFs could use a standard feature of the PDF specification to run attack code hidden in the file; he also demonstrated a way to modify an Adobe Reader warning message in order to further trick users into opening such documents.
If I recall correctly, and a post in the Stack Overflow thread "Safely opening .txt files" supports my recollection, the only safe file type is .txt, but I could be mistaken.