When navigating to the Xilinx Licensing Page here and attempting to generate a Vivado WebPACK License, the Vivado WebPACK license is grayed out under "Activation Based Licenses".
Vivado WebPACK licenses are now all activation based and must be generated by first installing the tools and then following the below flow:
2013.4 and earlier: Open the Xilinx License Configuration Manager, Select the "Acquire a License" Tab, Select the "Get Free Vivado/ISE WebPack License" radio button, click "Next", and click "Connect Now".
2014.1 and later: Open Vivado License Manager, Select "Obtain License", Select "Get Free Licenses - Vivado WebPACK, SDK, free IP and more", Select "Connect Now".
After clicking "Connect Now", you should be taken to your account licensing page where your Activation Based WebPACK license will no longer be grayed out.