As of 2015, Windows 8.1 is compatible with Microsoft Office 2007 and newer editions. Microsoft have discontinued support for Microsoft Office 2003 and older, making those products unsupported and officially incompatible with Windows 8.1.
Attempting to install Microsoft Office 2003 or older versions on Windows 8.1 by using a compatibility mode setting for a previous version of Windows may work; however, Microsoft doesn't support this action. Use of discontinued Microsoft Office software makes Windows more vulnerable to security threats and is not recommended.
The extended support cycle for Microsoft Office 2007 Service Pack 3 ends in October 2017. Although Windows 8.1 is compatible with Microsoft Office 2010, compatibility issues have been reported with Microsoft Visio. If in doubt, check on the Windows Compatibility Center before purchasing or upgrading to a later copy of Windows.