Visual studio has it's own integrated web server, so, no it's not mandatory to install IIS for development. However, once you decide to deploy a project you will need IIS.
For more information's about Web Servers that can be used in development in VS read this:
http://msdn.microsoft.com/en-us/library/58wxa9w5.aspx[
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Meanwhile for deploying an ASP.NET project on IIS check this nice CP article:
Deploying ASP.NET Websites on IIS 7.0 [
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Cheers