You can also achieve this in Office versions as recent as 2013 by opening a document and going to File -> Options -> Trust Center (along the left-hand side) -> Trust Center Settings ... (on the right-hand side) -> File Block Settings (along the left-hand side) and unchecking the boxes in the Open and Save columns for the types of files you want to open.

You can also use this to do hilarious things like preventing Word 2003 from opening and saving native docx files.