I have tried many many many media players in the last decade and without hesitation I can tell you that JRiver is the best media center application I have ever tested and used. There are so many reasons why this is, it comes down to minor details more than anything. What sets it apart are the codecs, the options, the ability to use every piece of media or files you can think of with it - Movies, Pictures, PDFs, built in HDTracks and many other music/movie stores. It has WASAPI, ASIO, Kernel Stream and many more. You can customize almost every aspect of it like Foobar except even better.
It has different modes such as Theater Mode which is like an xbox media center style way of browsing your files and listening to music or watching movies/tv. I just can't recommend it enough, after using it for a few months you will notice some of the little things and respect the program a lot more day by day.
Of course JRiver is basically a Windows only program, it has a beta app out for Mac, but not sure how well it works at the moment. For linux there are a few great options, but none I'd feel comfortable choosing over another right now.