It should be noted that "Code Behind" is a feature of the Web Forms view engine. It really has nothing to do with ASP.NET MVC itself.
For example, the Razor view engine in MVC3 does not even support it.
I would answer your question this way: If you cannot switch view engines without rewriting your controllers (or even your models) then you are not using the MVC pattern correctly.
Probably most of what you are doing in the .aspx.cs file should really be done before the model (or View Model) gets passed to the view. That said, in projects that I have migrated from ASP.NET Web Forms to ASP.NET MVC, I left a lot of the Code Behind in place. For example, I find it cleaner and more pleasing to use a Repeater control than to try to use a 'for' loop in Web Forms. I am still just iterating over View Model data after all. So why not? Separation of concerns is preserved (perhaps to a greater degree in fact).
I mean, why should "best practice" for Web Forms suddenly be the wrong way to do a Web Forms View? As a simple example, consider a Repeater that assigns a different CSS class to every second row of a table. Why should my controller (or even my model) care? Trying to put this kind of logic inline in Web Forms quickly devolves into tag soup and complete spaghetti. Now imagine something more complicated.
I have left Master pages in place that build the menus in the code behind. Again, all data comes from the View Model. I do not see why using GridView or other controls in this way should be a problem either.
I usually disabled ViewState in Web Forms anyway and did the data binding in "Init". Still, there would often be a small ViewState that I could not get rid of. I put some code in "Render" that moves this to after the form (it defaults to before). When moving to MVC, I sometimes left this code in. So, I have ASP.MVC sites that do indeed use Code Behind. I am just careful that it code that is specific to the view.
On new projects, I generally have found less of a need for Code Behind on most pages. Thankfully, view engines like Razor have made mixing code and mark-up in-line a lot less painful to write, read, and maintain.