Storing custom objects in Sessions

Add it to a master page or you could add a static property to you ShoppingCart object

public static ShoppingCart GetCurrent
{
    get
    {
        if(HTTPContext.Current.Session["CurrentCart"] == null)
        {
            HTTPContext.Current.Session["CurrentCart"] = new ShoppingCart();
        }
        return HTTPContext.Current.Session["CurrentCart"] as ShoppingCart;
    }
}

ASP.NET session corresponds to browser session - it is independent of whether user is authenticated (logged in) or not. So you should not have any issue with regards to guest/member sessions. I would advise you to expose the current shopping cart via static accessor property - for example

Class ShoppingCart {

    public static ShoppingCart Current
    {
      get 
      {
         var cart = HttpContext.Current.Session["Cart"] as ShoppingCart;
         if (null == cart)
         {
            cart = new ShoppingCart();
            HttpContext.Current.Session["Cart"] = cart;
         }
         return cart;
      }
    }

... // rest of the code

}

Few things to consider here:

1. Whenever web application or web server recycles/restarts, your in-process sessions would lost. It means you need persist your session in database at appropriate point.
2. You may use out of process session storage (database or different server) - you have to mark your shopping cart class as serializable in such case. There is performance cost to out-of-process sessions. As such, you are already storing session in database, so IMO, you should use in-proc sessions making sure to write dirty sessions into the database as soon as possible.