Airplane! (1980)
So many moments from this film to list. Here's the short list. I apologize if this list doesn't quite do the film justice:

The "Saturday Night Fever" parody

Lieutenant Hurwitz (played by Ethel Merman), having a bad case of shell shock, thinking he's Ethel Merman and starts to sing.

Steve McCroskey's running gag with he picked the wrong week to quit so-and-so:
"Looks like I've picked the wrong week to quit smoking."
"Looks like I've picked the wrong week to quit drinking."
"Looks like I've picked the wrong week to quit amphetamines."
"Looks like I've picked the wrong week to quit sniffing glue."

Ted Striker, when asked if he can fly the plane: "Surely you can't be serious."
Dr. Rumack: "I am serious. And don't call me Shirley."

Rex Kramer pulling off a pair of sunglasses to reveal another pair of sunglasses on his face.

Rex Kramer to Steve McCroskey: "The plan is to build him [Ted Striker] up. Give him all the confidence we can. [to Ted Striker via speaker] Striker, have you ever flown a multi-engine plane before?"
Ted Striker: "No. Never."
Rex Kramer: "S---! It's a g-ddamn waste of time! There's no way he can land this plane!"

Kramer throwing a cigarette out the window, triggering an explosion outside. McCroskey winces at the explosion while Kramer is completely oblivious.

When Striker forgots to check the oil pressure on the plane, leading to an explosion, he fears that "when Kramer finds out about this, the s--- is gonna hit the fan," which literally happens soon after.

Back to the Future (1985)
1950 Doc Brown's reaction when he asked Marty McFly who is the U.S. President in 1985.
Doc: "Ronald Reagan?! The actor? Then who is vice president, Jerry Lewis?"

The skateboard chase scene.

When Biff shoves Lorraine and mockingly laughs, George McFly throws a punch at Biff.

Just when Marty is about to fade away, George pushes an idiot away from Lorraine and kisses her, which restores Marty's existence.

Marty performing "Johnny B. Goode," prompting Marvin Berry to call his cousin Chuck: "You know that new sound you're looking for? Well listen to this! [holds out receiver to the band playing on stage]"

Marty saying goodbye to his parents before leaving the school dance and his attempt to time travel back to 1985.

Benny and Joon (1993)
Sam reenacting Chaplin's dance of the rolls routine from The Gold Rush (Charlie Chaplin, 1925) and other routines in the diner.

The Buddy Holly Story (1978)
Buddy Holly and the Crickets first performing at the opening roller rink scene with "That'll Be the Day."

The performance at the Apollo Theatre met with skepticism but quickly faded upon hearing Holly sing.

The last performance starting from a poignant "True Love Ways" to an upbeat medley of "That'll Be The Day," "Oh Boy," "Peggy Sue," "Maybe Baby," and "Not Fade Away." Holly's last line to the screaming audience "I'll see you next year" ends with the audience soundtrack suddenly cut off and freeze-framing the last image of Holly.

City Lights (1931)
The scrawny Tramp up against his brawny opponent in a boxing match. You just want to root for the underdog Tramp, even though he isn't quite successful.

Definitely the last moment when the once blind girl who can now see learns the identity of the Tramp.

Harry Potter and the Chamber of Secrets (2002)
Harry writing to Tom Riddle in Riddle's diary (reminicent of a chat room) and the flashback sequence as written in the diary.

The showdown between Harry and Riddle.

Harry Potter and the Prisoner of Azkaban (2004)
Hermione throwing a deserved punch at Draco Malfoy.

Harry attempting to drive away the Dementors from him and Sirius Black.

History of the World Part 1 (1981)
Moses presenting the 15...er, make that 10 Commandments because he dropped the third tablet with 5 commandments.

Moses raises his staff to part the lake for Comicus and friends to escape. Then it turns out that Moses' arms were up because he was being held up and robbed.

The Spanish Inquisition musical sequence.

Jesus of Nazareth (1977 miniseries)
The Annunciation with Mary receiving God's message in a beam of light from her window. If you're expecting the angel to appear with wings and a halo, you won't find it in that scene.

Jesus telling the Prodigal Son parable, motivating Matthew and Simon Peter to reconcile.

From the scourging at the pillar to Jesus emerging out of the stark white light in front of Pontius Pilate to the crucifixion to the Pieta to the very end. My eyes welled up throughout the film but two particular moments where I uncontrollably cried were the white light scene (that was when I started losing it) and the crucifixion scene. The latter moment with Robert Powell's (Jesus) eyes bulging out and mouth open, saying his last words as his life rapidly drained out of him was when I finally lost it. The sight of it and how he said his lines were very overwelming enough to leave me emotionally drained to the end.

Also at the very end, when Mary Magdalene tells the disciples she had witnessed Jesus' resurrection. When her claims were dismissed as "women's fantasies," how Anne Bancroft (Mary Magdalene) responded was so perfect: "Women's fantasies? Was his [Jesus'] death a fantasy? I saw him die!"

The Kid (1921)
The Kid throws a rock at a window and leaves quickly as soon as his foster father shows up to repair said window.

When the welfare and police officers take away the Kid and Chaplin fights them desperately to get him back.

Lupin III: The Castle of Cagliostro (1979)
The car chase with Princess Clarisse, Count Cagliostro's henchmen, and Lupin and Jigen all in pursuit.

The Chaplin-esque clocktower battle between Lupin and Count Cagliostro.

The Lord of the Rings: The Return of the King (2003)
Sam to Frodo: "I can't carry it [the ring] for you but I can carry you!"

Mahler (1974)
Gustav Mahler's conversion from Judaism to Catholicism, first portrayed as a silent film and switches to talkies when Mahler had converted and conducts Cosima Wagner in singing "Ryde of the Walkyries."

The Man Who Knew Too Much (1934 original and 1956 remake)
(1956 remake) Ben McKenna asking his wife Jo to take pills before telling her their son Hank had been kidnapped and Jo's reaction.

The Royal Albert Hall assassination attempt sequence, effective in the 1934 original and still effective in the remake. No matter how many times I see this scene or even hear the music played, Arthur Benjamin's "Storm Clouds Cantata," I still have my stomach in knots when I see or hear it.

Moulin Rouge (2001)
The musical numbers "Spectacular Spectacular," "One Day I'll Fly Away" and "Elephant Love Medley"

The "Come What May" number later ending with Satine's death.

North by Northwest (1959)
The opening credits, specifically the opening theme.

The crop-dusting scene.

The Mount Rushmore sequence.

The Phantom of the Opera (1925)
The Phantom dropping the chandelier. The anticipation of what will happen is chilling.

The famous unmasking scene. Though it may look tame by today's standards, it's still frightening, particularly how The Phantom reacts on being stripped of his mask.

The Princess and the Warrior (2001)
Sissi's emergency trachemony scene. Though it's disgusting and grotesque, Sissi becomes enamoured of Bodo, who is desperately saving her life. A variation of the fairy-tale kiss, it's also an awakening for the sheltered Sissi, who begins her search of Bodo after recovering.

The Princess Bride (1987)
The swordfight between the man in black/Westley and Indigo Montoya. "There's something I ought to tell you: I'm not left-handed!"

Indigo to Count Rougen: "I want my father back, you son of a b----!"

The Producers (1968)
Leo Bloom: "I'm wet! I'm hysterical and I'm wet!" [after being smacked by Max Bialystock] "I'm in pain! And I'm wet! And I'm still hysterical!"

At the Lincoln Center in New York, Leo has to decide whether or not he should join Max in finding a flop.
Leo: "I want... I want... I want everything I've ever seen in the movies!"
Max: "Leo, just say you'll join me!"
Leo: "I'll do it!" [behind him, water bursts out from the fountain on cue]

The "Springtime for Hitler" number.

Psycho (1960)
Marion's drive in the rain before stopping at the Bates Motel.

The shower scene (natch and nuff said)

The second murder, the revelation of the murderer, and Norman's ending monologue inside his head.

Rear Window (1954)
Lisa investigating Mr. Thornwald's apartment when Mr. Thornwald himself shows up while Jefferies looks on helplessly in horror.

The light under Jefferies' door turned out shortly before Mr. Thornwald shows up.

Sailormoon R the Movie (1993)
The Sailor Senshi blasted away by Fiore in the streets in contrast to the eerily calm background music.

The senshi remembering when they were alone while Sailor Moon is tortured by Fiore.

The final confrontation from Mamoru/Prince Endymion/Tuxedo Kamen throwing the rose at Fiore to the flashback with little Usagi's rose to little Mamoru to the "Moon Revenge" battle scene to the very end.

Sailormoon S the Movie (1994)
Sailors Uranus, Neptune, and Pluto confronting the snow dancer early in the movie. This was the first time I saw the Outer Senshi in action, along with their transformation sequence.

Luna turning human and her flight with Kakeru to outer space.

Shadow of a Doubt (1943)
Uncle Charlie's unsettling rant about rich widows with the camera gradually closing in on his face.

The conversation between Uncle Charlie and young Charlie in the 'Till Two bar.

NOTE: For additional fave Trek moments, see also Favorite Dr. McCoy Moments

Star Trek II: The Wrath of Khan (1982)
A lot of great moments from this film. Among them:

Kirk referring to Spock's "death" in the Kobiyashi Maru simulation: "Aren't you dead?"

Khan's first attack on the Enterprise.

Kirk: "KHHHHHHHAAAAAAAAAAAAAAAAAAANNNNNNNN!" Somewhat disproves the phrase "In space, no one can hear you scream."

The last half-hour or so: the cat-and-mouse game Kirk and Khan play in the Mutara Nebula, Spock mind-melding McCoy ("Remember"), the desperate escape from the Genesis detonation, McCoy to Kirk "Jim, I think you better get down here," Spock's death scene, Kirk's eulogy, Kirk reconciling with his son David, Kirk's last log entry ("There are always possiblities"), Spock's coffin on the Genesis planet and the epilogue.

Star Trek III: The Search for Spock (1984)
Kirk and crew stealing the Enterprise. You know Kirk will escape from the spacedock's doors and from the pursuing U.S.S. Excelsior but it's so fun to see that scene, along with the excellent score, in action.

Kirk's reaction to David's death.

The destruction of the Enterprise followed by Kirk and friends witnessing its fall:
Kirk: "My god Bones, what have I done?"
McCoy: "What you had to do, what you've always do: turn death into a fighting chance to live."

The return of Spock, especially the dialogue between Kirk and Spock. "Jim. Your name... is Jim."

Star Trek IV: The Voyage Home (1986)
A lot of good moments in this one too:

After arriving in 1986, Kirk asks where they are, Spock answers, "Judging from the pollution content, I believe we have arrived at the latter half of the 20th century."

Driver to Kirk for jaywalking: "Watch where you're going, you dumba--!"
Kirk: "Well, a double dumba-- on you!"

Spock's attempts at using "colorful metaphors" are hilariously deadpan. Among those attempts:
Gillian Taylor catches Spock for swimming along with the whales (he actually was trying to mind meld with them):
Gillian: "You were messing with my tanks and messing with my whales."
Spock: "They [the whales] like you very much but they are not the hell your whales."
Gillian: "I suppose they told you that, huh?"
Spock: "The hell they did."

Gillian Taylor (to Kirk and Spock): "Do you guys like Italian [food]?"
Kirk: "Yes."
Spock: "No."
Kirk: "Yes."
Spock: "No."
Kirk: "Yes. I love Italian." (to Spock) "And so do you."
Spock (to Gillian): "Yes."

After the Probe leaves and Earth is saved, Kirk and crew celebrate by splashing about in San Francisco Bay.

Kirk demoted from admiral to captain and awarded as the new captain of the Enterprise.

Spock and his father Sarek making amends with one another. Sarek admitted he once objected to his son Spock joining Starfleet but was proven wrong.

Kirk on their newly assigned ship the Enterprise-A: "My friends, we have come home."

Star Trek VI: The Undiscovered Country (1991)
[When Spock could not find the location of the peace conference from mind-melding Valeris]
Scotty: "Then we're dead."
Spock: "I've been dead before."

Racing against time to stop the next assassination attempt at the peace conference: Sulu's "Fly her apart, then!" line, Spock and McCoy creating a special photon torpedo to track General Chang's cloaked Bird-of-Prey and literally blow his cover, Scotty kicking down the door and shooting the assassin, Kirk explains about the undiscovered country referring to the future and how people are afraid of change.

Spock on the Enterprise to be decomissioned: "If I were human, I believe the response would be... 'Go to hell.' (pause) If I were human."

Kirk's Peter Pan quote and last log entry, followed by the signatures of the Classic Trek cast. This is the big finish for the last film of the original crew.

Star Wars Episode III: Revenge of the Sith (2005)
Babies Leia and Luke brought to their respective homes, with the reprise of the "Binary Sunset" theme on Tatooine. That is where we came in.

Star Wars Episode IV: A New Hope (1977)
Han Solo coming to the rescue and Luke firing at his target into the Death Star.

Star Wars Episode V: The Empire Strikes Back (1980)
Luke facing Darth Vader during Jedi training with Yoda and seeing his own face on Vader's helmet after decaptiating him.

Before Han Solo is frozen into carbonite:
Leia: "I love you."
Han: "I know."

The showdown between Luke and Darth Vader and the infamous revelation ("I am your father").

Star Wars Episode VI: Return of the Jedi (1983)
The Ewoks are startled to see C-3PO (thinking of him as a god), leading one Ewok to confide to another about him in their native language. If you listen closely, their language is actually Filipino in the Tagalog dialect. Not exactly an effective moment per se, but I get such a kick out of it.

The final confrontation between Luke and Darth Vader, particularly when Luke refuses to kill his father and nearly paid for it with his life until Darth Vader literally overthrew the Emperor to his death.

Vader unmasked as Anakin Skywalker and reconciling with Luke before death.
Luke: "I've got to save you."
Anakin: "You already have, Luke."

The funeral for Vader and the ending celebration, along with Luke seeing the spirits of Obi-Wan Kenobi, Yoda,... and Anakin.

Strangers on a Train (1951)
The audience turning their heads during the tennis match except for Bruno Anthony, who keeps a fixed stare.

Guy desperately finishing his tennis match while Bruno tries to retrive his cigarette lighter. You root for both, even if one of them is the antagonist.

Guy and Bruno fighting each other on a carousel spinning out of control.

Superman (1978)
Clark Kent runs to a phone booth to change into Superman, only to find the booth an open kiosk and not a fully enclosed booth. (Clark later used a fully-enclosed phone booth in Superman IV: The Quest for Peace). Clark then runs across the streets to change through a revolving door.

The helicopter sequence:
Superman, catching a falling Lois Lane: "Easy, miss. I've got you."
Lois Lane: "You've got me? Who's got you?!"

Lois' interview with Superman (asking his height: "How big are you- How TALL are you?") followed by the flying scene (best romantic moment ever).

(2001 extended DVD release): Superman talking with the hologram of his Kryptonian father Jor-El after his first night of superhero feats. Jor-El reminds him not only to keep his powers in check but to keep his true identity a secret. Most poignantly, the scene ends with Superman trying to embrace his father, even though Jor-El appeared as a hologram and had died a long time ago.

The 39 Steps (1935)
The climatic music hall scene, which also revealed the MacGuffin. Now, now, I won't tell you if you haven't seen it yet.

To Be or Not To Be (1942)
The running gag of Lieutenant Stanislav Sobinski leaving his seat upon hearing the words "to be or not to be," his cue to meet actress Maria Tura backstage.

Joseph Tura's disguise as Concentration Camp Erdhart.

The shooting of Professor Siletsky on stage just as the curtains are raised.

Torn Curtain (1966)
Michael Armstrong finding it difficult to kill an East German policeman. The wife of Armstrong's contact tries stabbing the policeman, whacking him in the legs with a shovel, and finally stuffing his head in the oven. This inspired Joel and Ethan Coen's directorial debut Blood Simple (1985), specifically when Ray tries to clean up and dispose Marty's corpse.

The Untouchables (1987)
The recruiting of George Stone/Guiseppe Petri

The "enthusiasms" speech by Al Capone whilst holding a baseball bat at the dinner table. If you've seen this movie, you know what happens. If you haven't seen it, let's just say someone at that table will become the baseball to his bat.

The death of Jimmy Malone.

The Grand Central Station shootout scene. Bloody but stylish and suspenseful homage to the Odessa Steps massacre scene from The Battleship Potemkin (Sergei Eisenstein, 1925)

Vertigo (1958)
The opening credits with Saul Bass' intricate designs accompanied by Bernard Herrmann's haunting score.

Judy Barton appearing as a dead ringer for Madeline, bathed in green light eminating from the neon green sign outside her window looking like an apparition. When she steps out of that light and appears in normal skin tones, Scottie in a sense did the impossible: bringing back the dead.

Scottie in an unsettling confrontation with Judy at the tower.

Written on the Wind (1956)
Marylee Hadley dancing erratically and orgasmically to frantic music while her father dies of a heart attack.

Kyle Hadley confronting long-time friend Mitch Wayne at gunpoint for knocking up his wife Lucy Moore.

Way Out West (1937)
The famous softshoe dance sequence and "In the Trail of the Lonesome Pine."

Young Frankenstein (1974)
This film also has many moments to list. Here are a few:

Dr. Frederick Frankenstein accidentally stabbing his leg with a scapel in class.

Igor tells Dr. Frankenstein to "walk this way."

[Dr. Frankenstein, while holding Inga, sees Igor knocking on the door with the huge door knockers on it]
Dr. Frankenstein: "What knockers!"
Inga: "Oh! Sank you, doctor!"

Igor and Dr. Frankenstein carry a coffin out of the grave.
Dr. Frankenstein: "What a filthy job!"
Igor: "Could be worse."
Dr. Frankenstein: "How?"
Igor: "Could be raining." [starts to rain]

The "Puttin' on the Ritz" number

Elizabeth trying to fend off the monster's advances but succumbs to them: "Oh, sweet mystery of life! At last I found you!"