Does Word 2013 have version control?

File → Info → Versions → Manage Versions is where it's at in 2010. I don't have 2013, but I have to imagine it'd be the same.

Versioning is available for all documents stored in OneDrive. In fact, it works just as it used to in Word. You see the document stack with the latest version on the top, but you can restore an earlier version, which moves the restored version to the top of the stack.

If you don't have problems with storing documents online, simply use OneDrive... or use OneDrive selectively as part of your content creation process. Plus, it preserves versions for Excel and PowerPoint.

You're probably looking for the Always create a backup copy feature in Word Options > Advanced

It'll create a backup file every time you save.

However Windows already had support for previous versions, no need for office itself to have version control. From Windows 8 onward the feature has been replaced with File History

Still you do need to set up that first before it backs up your file

If you're using OneDrive then you can also use its history feature