Magento recommends Linux for hosting Magento.Please refer following links for the system requirements.
I will not suggest you to use windows server for production site. Though you can use windows server for Magento but I suggest you to use it till development server only.
while i have never tried that myself, but if php application is running on windows servers, then magento will do, if you have skills you can do this...
I agree with the others that Magento can run in Windows server as long as all the required software like the Web Server, PHP and MySQL are present but it is not recommended as it is not meant to be running in a Windows environment so you may face more compatibility issues than it is worth it.
You can run magento on Windows but it is not optimized. Magento don't require OS but the software under it will require. For example if you want to use Varnish cache for magento then you have to install it on Unix OS.