OK, a worthy challenge. Jason offered up some interesting choices, a bit on the blood-spattered side, perhaps, but an ambitious list nonetheless.
Afraid I don't have Jason's powers of cinematic recall. So here are three of my top scenes:
Call it, from No Country for Old Men. Javier Bardem is such a deliciously wicked jackal, toying with the life of an everyman. When he tosses a quarter and tells the store clerk to "call it," there is no doubt Bardem is ready to whip out his compressed-air killing machine if the call is wrong. This rivets because of Bardem's brilliant depiction of psycho-assassin Anton Chigurh, calmly munching cashews as he plays out his deadly game, and the terse writing of the Coen Brothers. Watch it, and feel your gut tighten into a very hard little knot.
A brief and final encounter, from The Way We Were. Former lovers Barbra Streisand, the commie, and Robert Redford, the capitalist, meet again through happenstance. The embers of all that went before are stirred for a few last, aching moments. As you watch these two icons, you can't help but wonder: What might have been? Streisand and Redford create more chemistry than a Chevron research lab. The scene is heart-rending without being schmaltzy.
The last gunfight, from Shane. Alan Ladd's finest role. He's the tight-lipped gunslinger who rides into the valley to protect the homesteaders from the ranchers and their sociopathic enforcer, played by Jack Palance. The final shoot-out may be predictable, but that doesn't make it any less satisying. Stand up, applaud, and throw some popcorn. Classic finale to a classic Western.
There are others that come to mind as honorable mention: Horse's head, from The Godfather, You Talkin' to Me? from Taxi Driver, and the opening monologue from Patton, among them.