True story: I answered an advert for a crowd scene being filmed at the Lincoln Memorial, for Milos Forman's film of the musical 'Hair'. They filmed a bunch of folk (couple of thousand of us showed up), and if the final film had let the crowd scene run under the end- credits for juuuust a few seconds more, I would have made my Hollyweird debut.
C'est la vie.
At least I got to see the filming of another scene (cut from the release), and was entertained by comedian Robert Klein before the filming; after the filming, there was a performance by this young, red-haired singer I'd not heard of before, named Bonnie Raitt.

Not technically an extra, but there's a guy in Jaws in the scene where the fishermen have a shark they caught hung up on the dock. Richard Dreyfus says something like the latin name for the species and the guy says "a whaaat??" in a very high, soft, gladly pay you next tuesday for a hamburger today kind of voice, and then 30 seconds later they cut back to him and he's like an 80s cabbie stereotype: "Don't give me this bite radius crap, Stick your friggin head in there."

Gets me every time

the guy who wore the Alderaan costume in Star Wars IV, talk about dedication to your role