Per the documentaiton on the installer download for .NET 4.0 ( http://www.microsoft.com/download/en/details.aspx?id=17851)
Additional Requirements for Server
Installation
If you have to perform a server
installation, your computer must have
the following software in addition to
the basic requirements:
•Internet Information Services (IIS)
version 6.0 or later. To access the
features of ASP.NET, IIS with the
latest security updates must be
installed before the .NET Framework is
installed. ASP.NET is supported only
on Windows XP Professional, Windows
Server 2003, Windows Server 2008, and
Windows Server 2008 R2.
So it will run in IIS 6.0 or above. If you want to know which operating systems support asp.net 4.0, that would be any operating system that supports IIS version 6.0 or above. This jives with my comment on your question.
That said, the biggest thing to watch out for is that you have to configure any .NET 4.0 IIS application to use a different applicaiton pool than 2.0, 3.0, or 3.5. There's more info on this here: http://johan.driessen.se/posts/getting-an-asp.net-4-application-to-work-on-iis6