Does ASP.NET MVC require IIS? Could I develop an application that uses the new ASP.NET MVC framework on a client machine that does not have IIS installed?
You need IIS to get ASP.NET to work (MVC or WebForms). From what I know, it is ideal to have IIS 7 for MVC, but it is possible with IIS 6.
Developing a MVC application without IIS is possible, with the built-in web server integrated with VS 2008 (as been already mentioned), but for deployment, that is when you need IIS.
A browser is all that is required on the client machine.
IIS is not required on the developer machine according to the download page.
Visual Web Developer 2008 Express, or the regular editions of Visual Studio will include the Cassini web server for development.
I think what you're asking is if you were to develop an ASP.NET MVC application would you need IIS on your local dev machine to run it?
The answer is, no you don't.
In short ASP.NET MVC can technically be run by any web server that can allow the website itself to handle the requests instead of the web server handling them.