The scene in Boogie Nights where Dirk and pals are getting ready to rip off (and accidentally kill) a drug dealer. Dirk smiles through the drug-addled haze slowly as the enormity of the line he is about to cross weighs down on him. I think “Sister Christian” might be playing in the background. It isn’t long.
Same film: Burt Reynolds turns off the sound to the Colonel’s phone and walks away, as the Colonel desperately tries to get him to come back. There is dialogue, but none of us can hear it.
I would have to watch it again, but Children Of Men has a few good ones if I remember right.
Before Lucas messed with it, and it’s not an entire scene, but in Return of the Jedi, where Luke is all but helpless under the Emperor’s force lightning assault and Vader is just standing there looking between Luke and the Emperor.
Quite a lot of Wall-E
Indeed. On a related note this simple scene from SW has all heart ans emotion that all the CGI in the world can’t match.
Binary Sunset
The first 8 minutes of Up have almost no dialogue, but tell the entire story of a life from childhood to old age, with love, marriage, heartbreaking sadness and simple, lovely pleasures. I was moved to tears at least twice.
The whole film Jeremiah Johnson has very little dialogue and tells the story well without it. Also, one of the greatest (IMHO) films of all time, Lawrence of Arabia, has long stretches with no dialogue.
Another Godfather dialogue-less (except for the screaming) scene I like is the horsehead in the bed scene and then it cuts back to Don Corleone’s sitting room and Marlon Brando arches his eyebrows perfectly.
At one time I watched a bunch of silent movies and initially I thought I was going to be reading placard after placard but in reality there weren’t that many. It was astonishing how little the story relied on them and how much was conveyed by the acting.
The first three minutes of Touch of Evil is one long shot and dialogue free, and it’s still remembered as a classic piece of cinema:
The mirror scene in Duck Soup with Groucho and Harpo Marx. It’s hilarious.
The scene in The Piano when Helen Hunt and Anna Paquin are on the beach, and Hunt opens the piano crate just enough to play (the them song) and Paquin dances on the beach. It’s obvious that the piano is their only outlet and their best way of communicating, and it’s as if they are really just one person.
I was also going to mention the scene The Black Stallion, but was beaten to it.
Toward the end of the climactic fight scene in Way of the Dragon (U.S. title Return of the Dragon), there is a brief moment when Bruce Lee and Chuck Norris pause and just exchange glances. Neither actor says a word, but you can tell what both characters are thinking.
Just for trivia’s sake, mention should be made of The Thief (1952) where
When I saw this film back in the 50’s or early 60’s, I kept waiting for the first words to be spoken – in vain. Plenty of sound effects, including a ringing phone that you knew just had to be answered but which quit ringing just before it was picked up.
Unless you’re into gimmicks like “no dialog” you could safely skip this one! 
In Mario Bava’s Black Sunday there is a scene with a coach pulled by black horses goes thundering past, and it is done pretty much soundlessly so it comes off as extremely haunting. Here at about 7 minutes. It is very short, a minute or so only, but very strong.
The one scene that actually stuck with me from watching it as a young kid back in about 1968 or so was the scene used in a compilation show 100 Scariest Moments or some such title as that - which is about the first whole set of scenes where they are executing her.
This diving scene from The Deep is good. (This is the Spanish-dubbed version of the movie, but for the wordless scene, I guess it doesn’t matter.)
I don’t think anyone’s mentioned 2001. Pick a scene, almost any scene (although my first thought was the EVA to replace the AE35 unit, but the first 20+minutes have no dialogue, as well as much of the entire second half…).
Yeah, if this was a contest, you won.
Goodfellas, which inspired Boogie Nights, has a few too.
Holly Hunter
In fact, the best dialog-free scene from the Godfather films is the assassination of Don Tessio, from Part 2.