In a Microsoft Premier Field Engineering Platform blog post, the company flat out says that Windows 8.1 Update is a required download for Windows 8.1 users. The blog post states:
Failure to install this Update will prevent Windows Update from patching your system with any future updates starting with Updates released in May 2014 (get busy!)
Windows 8 users who have yet to update to Windows 8.1 don't necessarily need to also download this update, although it might not be a bad idea. Microsoft has already announced that it will stop supporting Windows 8 in the very near future. Previously, the company indicated that it will end support for Windows 8 two years after the launch of Windows 8.1, which would be on October 18th, 2015. Now a new FAQ page says that the final date for Windows 8 support has been moved back a few more months and it will now end on January 12th, 2016.