You can run an MVC application without installing MVC on your server. There is something called deployable dependency in Visual studio. That will publish your MVC DLLs in your bin folder when you publish it.
from the msdn page,
This will add assemblies (DLL files) to a Web site project or Web application
project. When you deploy your Web site or application, the files are
included in the deployed project. This is useful if applications or
technologies that your project depends on are not already installed on
the server that will host your Web project. For example, you can use
this feature to deploy an ASP.NET MVC 3 Web application to a server
that does not have ASP.NET MVC 3 installed.
Right Click on Project and Select Add Deployable Dependency from the context menu
Select what all DLLs you want to be published
After clicking OK, You will see a new folder called _bin_deployableAssemblies. You can do normal Publishing procedure now and you will have the dlls in the bin folder of the publish output.
Check this post for more details http://haacked.com/archive/2011/05/25/bin-deploying-asp-net-mvc-3.aspx
You should have Visual Studio 2010 SP1. Otherwise it will not be shown in the context menu when you right click on the project to be published.
EDIT :
As of MVC4, all necessary assemblies to run an MVC application are automatically added to the bin directory, and any MVC4 application is bin-deployable (means you can run it in a server without explicitly installing MVC) . For this reason, the Include Deployable Assemblies dialog has been removed from Visual Studio 2012
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