Parallels Desktop 7 for Mac and earlier versions
Please note that Parallels Desktop for Mac version 7 and earlier will not support Windows 8.1 as guest OS. To be able to run Windows 8.1 virtual machine in Parallels Desktop for Mac you should upgrade to Parallels Desktop 9 for Mac: http://www.parallels.com/store/
Parallels Desktop 8 for Mac
The latest update of Parallels Desktop 8 for Mac does support Windows 8.1 as guest OS and is available to address the majority of Windows 8.1 compatibility issues. There are known appearance issues with dynamic resolution and Coherence view mode. Please make sure that you have the latest update by downloading it here.
Parallels Desktop 9 for Mac
Full Windows 8.1 feature set support in Parallels Desktop 9 for Mac.