If the question is what is the most influential film for "film studies" and not "film" generally--then I think the answer has to be Rear Window. It is not only thematically a film about watching films--the ethics and politics of watching--but it also provided the ground for "film theory" itself was born, with Mulvey's landmark essay marking a new ... See Moreperiod in the study of film. It has been revisited since then by Robert Corber, Slavoj Zizek, John Belton, and many many more. It might not be the greatest film of all time (or even Hitchcock's best)--but as far as "film studies" go, you can't find a film that has been more influential.

"Breathless" and "Rear Window", as mentioned above by others, seem good candidates for any short list of most influential movies on film studies.

Additionally, I suggest Dziga Vertov's "Man with a Movie Camera" and Sergei Eisenstein's "The Battleship Potemkin".

Hmmm.... Not eligible for this, presumably, but I just wanted to put my two cents in for "Citizen Kane." Whether embracing the auteur theory or rejecting it, all film theories are post-auteurist, and Welles is the quintessential auteur. Film courses everywhere use it as a primer for how to read a cinematic text, with good reason. 'Cause it's great.

It depends on what generation of film studies you're talking about, but as a silent film scholar, I'll toss my hat into the contest for BIRTH OF A NATION, which is not a film that I like, but which has spawned numerous good & historically-informed books and essays about silent film history and race and politics. It also teaches really well -- its ... See Moreracism and popularity never fail to surprise students. There are lots of other contenders, of course: STAGECOACH, VERTIGO, REAR WINDOW and CITIZEN KANE (already mentioned by others), but you asked for one title.