I recently upgraded to Office 2013 and everything seemed OK at first. However, when I subsequently upgraded to Windows 10, Word 2013 started refusing to open files that had been emailed to me, which was a real nuisance since most of my work comes that way.
Clicking on the Help button in the error message led to scary stuff about possible corruption of the file I was trying to open. But why should everything I downloaded be corrupt, and why if that were the case was Word 2007 happy to open the same files?
Initially I worked round the problem by opening the files in Word 2007 and resaving them, which seemed to convince Word 2013 that they were OK. However, having dug about a bit, I have discovered that Word 2013 (combined with Windows 10?) has a new security precaution built in: it simply blocks all downloaded files!
To get round this on a file by file basis, you can go into File properties and manually unblock the file. But for me a better solution was to go into Trust Center (in Word options) and add my entire Documents folder and subfolders to Trusted locations. Problem solved.