But I can't help but think that's the wrong Doctor to appear in a classic Hitchcock film! Matt Smith wasn't the Doctor in 1958!
Okay, I know, time travel. And furthermore, NO ONE was the Doctor in 1958, technically. That's all besides the point. Here's a though experiment I often fall prey to (oh you didn't know this was a session of Geeks Anonymous? Me neither when I began writing):
Take any film (historical, sci-fi and horror work best, but you need not limit yourself) and materialize the TARDIS into it. The door opens, who comes out? The Doctor as played by the actor who WOULD have played him at the time. Hartnell scores everything before 1963 (probably with Susan if you're adding companions). Try to imagine the narrative with him in it. I bet there are other Whovians doing this - fess up! And role-players? That could be an easy hook for your Doctor Who-related games!
William Hartnell (beginning of time - 1966): Metropolis, The Birds, A Hard Day's Night
Patrick Troughton (1967-1969): Camelot, 2001: A Space Odyssey, Planet of the Apes
Jon Pertwee (1970-1974): Chariots of the Gods, Live and Let Die, The Towering Inferno
Tom Baker (1975-1981): The Stepford Wives, Close Encounters of the Third Kind, Alien, The Jerk
Peter Davison (1982-1984): Gandhi, Blade Runner, Brainstorm, Romancing the Stone
Colin Baker (1985-1986): Cocoon, The Goonies, Little Shop of Horrors (Colin can really sing!)
Sylvester McCoy (1987-1995): They Live, The Abyss, Jurassic Park, Forrest Gump
Paul McGann (1996-2004, though you may replace him in those later years with the War Doctor if you want): Twister, Shakespeare in Love, The Matrix, 28 Days Later
Christopher Eccleston (2005): War of the Worlds, Serenity, Munich
David Tennant (2006-2009): 300, Cloverfield, The Curious Case of Benjamin Button
Matt Smith (2010-2013): Inception, Midnight in Paris, The Hunger Games, Oculus
Peter Capaldi (2014 - ): The Grand Budapest Hotel, Crimson Peak, Ex Machina
Just examples. I actually do this with every movie on my shelf, as I zone off sometimes. What would be YOUR favorite movie-Doctor matches from the appropriate years?