A family of Microsoft word processing software products for creating web, email, and print documents.
Here is how I managed to fix the problem for me. I am using Windows 8.1 which is an upgrade from Windows 8.
First, go to Programs under Control Panel and remove any installation of Onedrive/Skydrive you might have. Some users said this sorted out all problems but for me it wasn't enough.
The next step I had to do is to use the Onedrive app that comes with Windows 8.1. For that I had to associate my Windows Account with a Microsoft Account. After that I configure my Onedrive to have all files available online only by default (which is my preferred method) and I proceeded to immediately disconnect this stupid [*] Microsoft Account integration and return to having my local account. I tested and now Word no longer crashes when trying to open files directly from Onedrive.
[*] One thing about Windows 8.1 that I despise is this annoying attempt of forcing users over and over again to associate their account with a Microsoft Account. This is particularly a pain if you want to use the built-in Onedrive app that comes with Windows 8.1 -- you can't use it otherwise! I find this extremely inconvenient for several reasons and I hope MSFT will get a grip for the next version of Windows.