.NET Framework 3.5 Service Pack 1
Currently any modern ASP.NET apps that are based on Abstractions layer still have to resort to HttpContext.Current to create HttpContextBase instance.
A good example is DynamicData which is the only present application of Abstractions. It internally depends on HttpContext.Current and hence it cannot be tested outside ASP.NET runtime.
(I'm unsure if ASP.NET MVC makes use of it; it uses different abstractions/routing assembly than .NET 3.5 SP1).
Providing HttpContextBase.Current which works almost similar to HttpContext.Current would solve couple of difficult situations to solve this kind of problem.
Or applications such as DynamicData should (have) expose(d) public HttpContextBase setter that is internally used by the framework.