First, it depends on what you consider a movie. If you define “cinema” as broadly as I do, then the answer is probably “countless.” So let’s pick something more discrete: feature films (which is what most people mean, anyway, when they say “movie”).
There’s no hard and fast rule as to what constitutes a feature. The term itself is a relic of theater-going: the feature film was the featured film—it was what the theater advertised outside, and presumably what compelled you to purchase a ticket and enter—as opposed to the various newsreels, cartoons, and serial installments that also ran (and then, eventually, stopped running). Theater-going in 2012 seems an increasingly old-fashioned hobby (see Roger Ebert’s recent article on declining ticket sales), but we still use the word to mean “a long film.”
But how long? The Wikipedia informs us:
The Academy of Motion Picture Arts and Sciences, the American Film Institute, and the British Film Institute all define a feature as a film with a running time of 40 minutes or longer. The Centre National de la Cinématographie in France defines it as a 35 mm film longer than 1,600 metres, which is exactly 58 minutes and 29 seconds for sound films, and the Screen Actors Guild gives a minimum running time of at least 80 minutes. Today, a feature film is usually between 80 and 210 minutes; a children’s film is usually between 60 and 120 minutes. An anthology film is a fixed sequence of short subjects with a common theme, combined into a feature film.
Let’s go with that 40-minute cutoff. Are we ready to start counting?