I am a beginner to the ASP.Net MVC. After reading many tutorials and digesting its concepts, I have yet to see an approach that clearly demonstrates where does the business logic go.
My app will have a lot of use of jQuery AJAX usage (which will be calling Controller's Actions for various purposes such as dependent interaction, validation). I will definitely use the ViewModel concept, but I am still unclear where the business logic should reside. I do not want to put in the controller or a model. Should I put it in a separate service layer?
I think you pretty much answered your own question, in a separate project.
Not in the controllers and absolutely not in the models.
Edit: Notice that the controller is highly coupled with the httpcontext so it will be a very smart thing to move the logic layer to a different dll-layer.