How do you access application variables in asp.net mvc 3 razor views?

Views are not supposed to pull data from somewhere. They are supposed to use data that was passed to them in form of a view model from the controller action. So if you need to use such data in a view the proper way to do it is to define a view model:

public class MyViewModel
{
    public string LicenseName { get; set; }
}

have your controller action populate it from wherever it needs to populate it (for better separation of concerns you might use a repository):

public ActionResult Index()
{
    var model = new MyViewModel
    {
        LicenseName = HttpContext.Application["LICENSE_NAME"] as string
    };
    return View(model);
}

and finally have your strongly typed view display this information to the user:

<div>@Model.LicenseName</div>

That's the correct MVC pattern and that's how it should be done.

Avoid views that pull data like pest, because today it's Application state, tomorrow it's a foreach loop, next week it's a LINQ query and in no time you end up writing SQL queries in your views.

You can get the current Application using the automatically generated ApplicationInstance property:

@ApplicationInstance.Application["LICENSE_NAME"]

However, this logic does not belong in the view.

@HttpContext.Current.Application["someindex"]

You should be able to access this via HttpContext.Current.Application[], however MVC best practices would state that you should probably consider passing this through your View Model.