Update Dec. 4 2012: The unsupported 64-bit Windows web player is not currently in working state in Unity 4.0.
While we have been developing Unity 3.4, we have ported the Unity runtime to the x86_64 architecture on Windows. You may have noticed that the Unity 3.4 editor allows "Windows 64-bit" as a new build option in the Standalone build. We have also ported the Unity Web Player to Windows 64-bit. This allows you to play Unity content in Microsoft Internet Explorer 64-bit or in 64-bit builds of Mozilla Firefox. Any Unity web content built with Unity 3.x should play in the 64-bit plugin. Content built with Unity 2.x will not work, as the 2.x runtime has not been ported to x86_64!
Without further ado, here it is!
Even though this is an unsupported product, please use the bug reporter which comes with Unity to report any issues you might have with the plugin!