The stereotypical movie zombie holds his arms out in front of them in the sleepwalk pose, shuffles slowly forward, and mindlessly mutters "Braaaaaains."

If there is a movie featuring zombies exactly like that, it's going to be surprisingly recent. The outstretched arms comes from Boris Karloff's The Mummy, though a lot of 40's and 50's era monster movies would depict whatever monster--Frankenstein, Dracula, whatever, reaching forward to grasp their victim.

The modern American pop-culture zombie basically begins with George Romero's Night of the Living Dead in which the zombies do move slowly, they don't say anything, and they aren't particularly associated with brains.

The brains thing comes from Return of the Living Dead whose zombies are hungry for brains, but these zombies are fully sentient, they're capable of solving problems, Tarman rigs up a winch to pull open a door, they can speak and understand English, one uses a radio, and depending on their state of decomposition they're able to move like normal humans.

28 Days Later features zombies that are fast and aggressive rather than slow and shambling. The Walkers from The Walking Dead don't speak at all and aren't specifically brain hungry. Other than very intentional parodies, I can't find a single film that depicts the stereotypical movie zombie.