Well, there's this:
It describes how to run an X application on one computer and have it display on an X server on another one.
Taking your title literally, you want to run an X client on your Windows computer, i.e.
to have an X application for Microsoft Windows displaying on a Linux computer. This can't be done as such, athough there are a couple of programs that will help you forward a Windows' desktop on your Linux computer.
If, on the other hand, you want to display an application on your Windows computer when it's running on Linux then you want to set up an X server on the Windows computer, and tell it to accept connections from your Linux computer. Then just run the program on Linux using the appropriate DISPLAY environment variable, as described in the HOWTO.
I don't know of any X-windows clients for Windows, but no doubt someone else will.