The most infamous issue. During project compilation or simulation, a background process named ning.exe (part of the ISE licensing and web update service) consumes an entire CPU core and never completes. This leads to perpetual "Running..." statuses.
Installing Xilinx ISE 14.7 on Windows 10 is a bit tricky. The software was originally designed for Windows 7 and 8, so you'll need to run the installer in compatibility mode. Right-click on the installer executable, select "Properties," and then check the box next to "Run this program in compatibility mode for:" and choose "Windows 7" or "Windows 8." This will allow the installer to run without any issues.