I'm going ol skool with my choices today, btw, does Hamlet count? What about Streetcar named desire? Cat on a Hot Tin Roof? I seem to lean towards plays turned to movies. Anyway...
Lady from Shanghai hall of mirrors speech. If you've seen it, you know exactly what I'm talking about. If you haven't seen it, its available on IW and its worth checking out. The Caine Mutiny when Bogart is testifying at his court martial trial. Another good one on IW. On the Waterfront coulda been a contender speech. Night of the Hunter love/hate speech and Robert Mitchum's insane "prayer".
There are a few in The Producers, Inherit the Wind, Vertigo, Dr. Strangeglove, To Kill a Mockingbird, Clockwork Orange and Elmer Gantry, too.
My favorites are Psycho (she wouldn't hurt a fly), West Side Story (How many can I kill Chino still have one left for me) and Brian's Song when Gayle Sayer's gives the locker room speech.
I'm going to have to say my personal number 1 is Lt. Caffey's (Tom Cruise) examination of Col. Nathan R. Jessup (Jack Nicholson).
Honorable mentions:
Billy Madison - The moderator's response following Billy's "rambling, incoherant response".
Big Lebowski - The first bowling scene which includes such great quotes as "the preferred term is asian-americans" and "This agression will not stand". (This movie would be my vote for most discussions).
Way of the Gun - Opening scene argument between the carrot top looking guy and Benicio Del Toro and Ryan Phillippe.
Navin R. Johnson: I know we've only known each other four weeks and three days, but to me it seems like nine weeks and five days. The first day seemed like a week and the second day seemed like five days. And the third day seemed like a week again and the fourth day seemed like eight days. And the fifth day you went to see your mother and that seemed just like a day, and then you came back and later on the sixth day, in the evening, when we saw each other, that started seeming like two days, so in the evening it seemed like two days spilling over into the next day and that started seeming like four days, so at the end of the sixth day on into the seventh day, it seemed like a total of five days. And the sixth day seemed like a week and a half. I have it written down, but I can show it to you tomorrow if you want to see it.
Christopher Walken in The Comfort of Strangers:
The monologue in the restaurant where he tells the couple about his father and his mascara, and having pissed and shat all over his dad's office after his sisters tricked him into drinking a laxative.
I always enjoyed Christian Bale discussing the complexities of Hewie Lewis and the News in American Psycho. But I do believe Quentin Tarantino is a genius when it come to this stuff, and must mention the many classic discussions used in Reservoir Dogs as well as Pulp Fiction, my favorite being "Personality goes a long way".
George C. Scott has a few in The Hospital -- (even in Patton, for that matter).
Scott again in Dr. Strangelove, in the war room. In fact, the same flick has several long actor's set pieces -- Slim Pickens reading the survival kit's contents to the crew, Sellers as Strangelove talking about preserving a nucleus of human specimens, Sterling Hayden's mag-fucking-nificent monologue about how he arrived at his theory "during the physical act of love" -- ("I do not avoid women, Mandrake. But I do deny them my essence.")
Marlon Brando's breakdown as he sits by his wife's corpse in Last Tango in Paris has some pizzazz -- or, at least, Brando makes it seem that way.
Another guy mentions Mitchum's left hand-right hand spiel from The Night of the Hunter, and he's so right.
Really, there are so many -- too many to remember or cite them all.
Andre Gregory in Malle's My Dinner with Andre is wonderfully close to being over the top. Christ, how do you make that stuff up?
David Thewlis in all of Leigh's early shorts with him, but especially in Naked. This one is over the edge, but if you can stand it, it is an amazing performance. It appears that he's vomited up this endless spew of verbiage on the spot. Chripesachord! Hats off to ya, fucker!
Delpy and Hawke in Before Sunrise. My heart is pounding just thinking about it.