Claire Trevor playing an alcoholic washed up singer in Key Largo, forced to sing for a drink. Apparently, part of her obvious reluctance was real - the director sprung it on her without warning. She won an Academy Award largely for that one scene.
Any scene Gary Oldman is in, in Leon the Professional.
Why don’t directors trust actresses to act?
L.A. Confidential
SPOILER IN CASE YOU HAVEN’T SEEN THE MOVIE, WHICH YOU SHOULD
When James Cromwell asks Guy Pearce if he knows who “Rollo Tomasi” is. Pearce’s reaction is one of the finest bits of acting I’ve ever seen.
Oh…unknown scenes? Ok.
James Brolin in Capricorn One. Second half of the film he’s got like a handful of lines but man does he go through hell for an hour.
Same with Sam Waterson when he’s climbing that mountain. I’d play that scene in my head whenever i rockclimbed.
In Veronica Mars Season 2 (I think) when she believes her father is on a plane that is going to explode and is trying call him.
She actually looks broken when the explosion happens.
The two that always come to mind immediately are both from Love, Actually. A silly movie with its share of problems, but:
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Liam Neeson’s look of anguish as he shoulder’s his wife’s coffin in the funeral scene. it’s a small, quick moment, but it gets me every time.
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Emma Thompson’s bedroom scene after she finds out about the necklace. It’s a master class in acting. At the end she nods to herself, wipes her eyes, straightens the bed cover and puts on a happy face for her family. Devastating.
It’s not an unknown scene since it is The Godfather but it’s one scene that probably no one would mention if asked about the movie.
When Michael confronts Carlo he is assures him that he won’t be harmed but he needs to hear Carlo confess that he set up Sonny. When Carlo confesses Pacino’s eye’s unfocus for a second and his whole body tenses slightly his whole demeanor changes subtly. He was sure Carlo did it. He was probably going to have him killed anyway. But until that moment he didn’t know for sure. Pacino could have raged at him. Pacino of today would have raged at him. Back then he was able to do the acting with his eyes.
I automatically translate the 1936 English into current English. 
I have one that’s pretty well hidden and obscure. The current Shadowhunters tv show is an awful angsty teen fantasy drama. My daughter likes it so I watch it. At least there are pretty people to look at.
In one episode two characters swap bodies. Harry Shum Jr plays a good guy named Magnus. Magnus is gay or at least in a gay relationship and the character is played with more than a bit of fabulousness. Alan Van Sprang plays the main bad guy Valentine. Although he started off as just menacing the character became more nuanced. Van Sprang is a very experienced character actor and it shows. When they did the body swap Van Sprang was able to subtly able to show the essence of the other character without turning it into a joke. In that moment I could see he was a good actor in an otherwise unchallenging role. His talent really shined through.
A couple of very understated moments you might have seen on TV:
A scene in Downton Abbey, where Penelope Wilton’s character is visited by Lord Wotsit who may well be about to propose. Just for a moment, someone who’s been composed and self-assertive all through lets just a tremble of one hand show a moment of girlish nervousness.
A showdown in Broadchurch 3, between Sarah Parish’s character and Julie Hesmondhalgh’s (her supposed best friend, who has just admitted she’d slept with her friend’s husband): Julie Hesmondhalgh has just a small twitch of the mouth which reveals, despite all that angst and her apologies, a flash of triumph over the “glamorous one” in their lifelong friendship.
Anything Mr. Robert Carlyle does onscreen. He is so amazing, I am overwhelmed, I would watch him in anything. On ‘Once Upon A Time’, as Mr. Gold, he beats up Maurice/Moe French with his cane, in a cabin in the woods until Emma finds him and stops him. It is excrutiating to watch, and the snarling Mr. Gold makes it impossible to look away. ‘Once Upon A Time’ is a Disney show and Disney never ignored dark sides of life, but this scene is way over-the-top just because of the look on Robert Carlyle’s face - rage, sorrow, anguish times ten.
I like the book version as well where Hagen is stunned that Michael is even going through with this rigamarole.
In Philadelphia Story, Macaulay Connors (Jimmy Stewart) gets drunk and drives to CK Dexter Haven’s (Cary Grant) house. Stewart hiccups and Grant says “Excuse me”. It was an improvised moment and you can see both actors trying hard not to laugh. Memorable for a different reason, I guess.
No dialog, not even much motion. The Last Picture Show when Cloris Leachman as Ruth Popper, the coach’s wife, realizes that Sonny isn’t going to be coming by for his afternoon canoodling any more. It’s no more than five seconds of her sitting on her bed in her dressing gown, eyes downcast. The pain is almost palpable.
It’s a silly show with mostly cartoon performances (or cardboard if it’s Jennifer Morrison) but Carlyle is brilliant literally every moment he’s on.
Good one.
There’s an incredible scene from the original Law & Order TV series, an episode called “Terminal,” in which DA Adam Schiff’s (played by the stellar Steven Hill) wife has a stroke and is on life support. At the end of the episode, [minor spoiler!!] they take her off of life support. (It is not clear if she will be able to survive without it). There is a moment of suspense as the heart monitor beeps, but then it falters and flatlines. We’re watching Schiff’s face the whole time, and as his wife dies his face twitches a bit and he lets out a tiny whimper. Blackout, end of show. It’s a really subtle bit of facial and vocal control - particularly powerful if you’re familiar with the show and what an irascible character he is. I find it heartbreaking.
Not an obscure film, but Absence of Malice is 36 years old (came out in 1981) and has two bits worth mentioning.
First is when the female lead (Sally Field) enters the room where Paul Newman is. Field has just done something that led to the death of a close friend of Newman’s, and his growled (and it sounds like a growl) “You don’t want to come in here.” along with the barely-repressed fury in his face is just damn impressive (the rest of the scene is good, too)
Second is something I consider as good a 5 minutes of film-making as you can do; from the time you see the feet of people (unidentified) until Wilford Brimley states “You have 30 days”, is just perfectly set, blocks, scripted, and acted by all the participants so well that you forget they are playing roles and they are all their characters and reflecting it.
IMHO as always. YMMV.
I’d also add the scene where Natalie Portman is crying through the door to Leon. That seems like such a hard scene to pull off without feeling silly or over the top.