Download and install the latest official Microsoft Xbox 360 Wireless package: http://www.microsoft.com/hardware/en-us/d/xbox-360-wireless-controller-for-windows
Download and extract this updated version of the device driver to someplace temporary: http://t.co/Z63uHmqM
Plug the receiver in. Windows will detect it and attempt to install a driver for it. If yours behaves as mine did it will NOT automatically match up with the official package you installed in step 1. Otherwise, you got lucky and you're done!
Choose the second option: "Install from a list or specific location (Advanced)". Click Next.
Choose the second option: "Don't search. I will choose the driver to install." Click Next.
If it shows you a list of hardware categories click Next first. Click "Have Disk..." and find the "xusb21.inf" file that you extracted from the archive in step 2.
If for some reason it comes up asking for additional files, choose them from the same location where you found "xusb21.inf" in the last step, in the "x86" (or "x64" if you're running 64bit Windows XP) folder below it.
If for some reason it asks for "WdfCoInstaller01005.dll" when "WdfCoInstaller01007.dll" is what you've got in "x86" you can insert the included driver CD and find it there. It was in "PC Driverx86" on my disk. It did this to me though it was a result of my earlier attempts to get the original driver working.
It should copy the files and then be done. If you receive a "Fatal error during installation" error my solution didn't work for you. Otherwise, click Finish and try syncing up your controller!