"Spider-Man! This is why only fools are heroes — because you never know when some lunatic will come along with a sadistic choice. Let die the woman you love... or suffer the little children! Make your choice, Spider-Man, and see how a hero is rewarded! Now choose!"
The Yu-Gi-Oh! card "Painful Choice", as the name implies, is all about putting your opponent in such a bind: you choose five cards from your deck, and he has to choose the one you get to keep (all the others are discarded to the Graveyard). Ideally, the player who uses this card is supposed to pick their five most powerful cards, meaning that whatever happens one of them is going to end up in his hand, and this card can combo with other effects that can result in the player getting all five cards regardless of what the opponent chooses. (Unsurprisingly, it's banned from tournament play.)
The real reason it's banned is because players usually use it not to get a card in their hand, but get them in the Graveyard. For example, the most notorious use of this card, was to use it to summon the incredibly powerful Black Luster Soldier - Envoy of the Beginning, possibly on your first turn. You chose any two Light Monsters, any two Dark Monsters, and any other card. No matter which card your opponent chose, you'd have the requirements to summon Black Luster Soldier; the choice your opponent made did not matter in the least. And there were lots of similar combos that could be used with a similar strategy.
This was used in a duel in the anime by Kaiba's adopted father. The five cards in question were the five pieces of Exodia, which he then used to summon Exodia Necros, a particularly nasty card that is immune to various things depending on which part/s are in the graveyard. All five being in there, it was immune to damn-near everything.
Kaiba's Expy in Yu-Gi-Oh! GX Manjyome also used this card in a duel with his brother. Since Manjyome needed a certain Spell card, and his brother was a total amateur who believed Attack Points were everything, he offered the Spell and 4 Monsters as a choice, knowing his brother would let him keep the one card that wasn't a monster.
In Magic: The Gathering, there's Choice of Damnations, which forces your opponent to pick a number. You then choose whether they lose life equal to that number or if they sacrifice cards they control until they're left with only that number of cards in play. Obviously, if they pick a number too low, you just force them to go on with only a few cards in play, but if they pick one too high their life can get dangerously low.
Another example is Gifts Ungiven. Gifts Ungiven lets you get any four cards from your deck (although they can't be duplicates). Then your opponent has to pick two to go into your hand, and two to go into your graveyard. Most decks that use Gifts Ungiven exploit this, by choosing four cards that ensure you get what you want no matter what the opponent picks.
And now the Archenemy rules contain a variation: some of the Schemes leave you with the choice of taking a big hit yourself or diluting the pain between your allies so nobody takes a big hit but the total damage is probably higher. (Admittedly, if you're playing a black deck, you'll probably always dilute it because that's how Black rolls.)
Lore from the Avacyn Restored block has an example. Liliana Vess captures Thalia's companions and instructs her to destroy the Helvault (the magical prison housing a great many powerful demons, one of whom Liliana wants to have a word with) or let them die. Surprisingly, she chooses to release the demons. Ultimately it is a subversion of the trope since Avacyn, the angel protector of the plane, had also been trapped there, so things end up getting better.
The Born of the Gods set introduces creatures with the "Tribute" ability. When one enters the battlefield, the opponent has the choice of either giving it some +1/+1 counters or triggering a nasty effect.
The Star Trek: Deep Space Nine expansion of the Star Trek CCG has a card, based off of the episode "Move Along Home", entitled "Pick One to Save Two". In the episode, Quark must choose one of his three pieces to "die" in order to allow the other two to continue. This card, a dilemma, presents much the same choice.
Early on in Upperdeck's Marvel/DC crossover card game using the "VS System", there was a card named Sadistic Choice, which was only usable by players using Spider-Man villains and had an illustration showing the Green Goblin and Gwen Stacy.
"Lesser of Two Evils" and "Legion of Losers" were similar to "Sadistic Choice."
The Star Trek CCG had a card called "Raise the Stakes" that gave the effected player a choice: either forfeit the game immediately, or risk having to permanently hand over a card from their deck to their opponent should they lose the game. Notably, this is the only card from this game that was banned from tournament play.
Parodied in Dilbert: In one strip, Phil the Prince of Insufficient Light comes up to Dilbert and sentences him to choose between the following two options: a highly paid yet utterly meaningless job whose results vanish before his eyes or a very low paid yet rewarding job that grants him the respect of his coworkers. Dilbert gleefully states that both options are better than what he has right now and calls Wally over to "get in on this".
And then when you arrive at Banshee, your ship crashes. The can breaks, the evil is unsealed, and the Sadistic Choice (or Heroic Sacrifice) is for naught.
This loses a lot of impact if your group also plays Paranoia and frequently kill each other at the drop of a Commie's hat.
Chess is full of Sadistic Choices. Moves known as "forks" are when a piece threatens two (or more) enemy pieces at the same time. Sometimes the player can Take a Third Option by using one to defend the other, or use a third piece to defend them both. Most of the time though, they have to sacrifice the less valuable one.
And then there's a zugzwang, a sadistic choice where every option will get you screwed. You can benefit from breaking a fork (if your opponent was expecting you to waffle, you can score a tempo advantage). You never benefit from a zugzwang.
The Splat book The Book of Vile Darkness details a particularly sadistic creature called the Eye of Fear and Flame who's only purpose seems to force mortals into choices like this. The example it gives is this: It might approach two young lovers in a forest and tell one of the to kill the other, or it will kill both of them. The only third option to this creature's demands would be challenging it and killing it. (Which actually isn't hard for most seasoned adventurers, seeing as it only ranks a CR of 8, but as the above example shows, it rarely targets victims who are capable of defending themselves.)
In Tomb Of Horros and most adaptations, this sort of thing arises if any heroes actually make it to confront Acererak. The heroes have two choices that lead to one of two endings, one where Acererak escapes to a different world but the heroes release thousands of souls trapped in his phylactery; (and it would take years for him to regain his power); or one where the heroes destroy the phylactery with Acererak in it, destroying him but condemn thousands of innocents to a Fate Worse than Death. A Golden Ending does exist in Return to the Tomb of Horrors, where the heroes can slay him and free all the souls, but this requires killing every single undead in the Fortress of Conclusion; including one he specifically set up near an escape pod; and then dissolving his phylactery. (This is actually considered to be the canon ending.)
Redcloak presents O-Chul, his paladin prisoner, with a Sadistic Choice in strip 545: tell him how Girard's Gate is protected, or Redcloak will throw a large group of hostages into an interdimensional rift to be devoured by the Snarl. Subverted in that since O-Chul genuinely doesn't know the gate's protections, all O-Chul can do is make peace with what's about to happen...
Another Goblins example occured before the story began: When Chief Kills-a-Werebear dies in combat and the goblin clan needs to elect a new chief, the clan fortune teller prophecises that if Kills' son becomes the new chief, he'll doom the clan to obscurity with his poor leadership. If Thaco is made chief, he will be a wise leader, but many goblins will want Kill's son to become chief anyway and he'll have to lead the clan through a brutal civil war. Thaco decides to exile himself from the clan so that the son can be chief.
In Khaos Komix, a gang of students will cut Charlie's hair so she can "wear a wig like a real tranny," or they'll vaginally rape Tom. It's no choice at all; by the time the first four meet her, Charlie's made the most of short hair.
There's a complicated example in The Fancy Adventures of Jack Cannon. Craig has kidnapped Angel. If Jack interferes with the hackers again, Gavin will kill Jack's parents. There are two villains at work here, both a part of the same organization. Neither has spoken to Jack personally to suggest the sadistic choice. However, the first guy may have broken some rules, which may mean that there is no need to Take a Third Option or make a choice. Not that Jack knows any of that.
This is analyzed in the webcomic City of Reality. The idea is, if the hero is given the choice of saving the girl, or saving a busload of children, what kind of person could he be if he chose to save the girl, if it meant that the busload of children died instead? Que a shot of the hero holding the girl tightly, telling the girl how much he loved her... while they both watch the busload of children drown, the girl wearing an increasingly horrified expression.
Independent YouTube film Caitlyn (Part 1Part 2) forces a sadistic choice on a girl about 9 years old. She wakes up chained to a pole with some rather tight looking bonds, and finds a handwritten note right in front of her informing her that she is holding the key to the bonds in her hand. If she frees herself, her parents will die. If she drops the key, she will be a prisoner forever. She drops the key. She wakes up in bed, but her parents are gone anyway. Talk about a Downer Ending.
SCP-516 is a sentinent tank that refuses to fire on unarmed sapient humans. So, naturally, one of the researchers orders someone strapped with explosives approach SCP-516 and blow it up, whilst handcuffed to an unarmed sapient human. The tank prodeeds to [DATAEXPUNGED].
The Nostalgia Critic is faced with one in the climax of To Boldly Flee: Return to his own universe where everything's scripted but he has a purpose in life, or step into the real world where he has free will, for better or for worse. Doug Walker notes that if he chooses the latter, he will doom his fellow critics to destruction since that universe is centered around him. He chose to stay and absorb the plot hole to save his friends.
Worm in Snare 13.04, Bitch is given one by Burnscar: kill her teammates, or fail the test and have Burnscar kill her friends and her dogs. She refuses, but Burnscar isn't able to kill them.
Alan Turing: After his work in Great Britain breaking the Nazi military codes, and devising the thought experiments that underlie any computer operation more involved than a pocket calculator, he had an affair that turned sour. In a time when homophobia was rampant, he was convicted of "gross indecency" for having "led his partner astray with his university education." He was given the choice by the judge to either go to prison or begin an antiandrogen regimen. At the time, he chose the latter. He committed suicide not long after.
The apportioning of available human organs to transplant patients in need of them comes down to this all the time, unfortunately. Likewise, whenever dialysis machines or other life-prolonging equipment are in short supply, life-and-death triage decisions may be necessary.
The 'winner' is usually the person who shows the most commitment to using their new organs wisely, meaning they quit drinking or smoking permanently, improve their diet or start making other healthy life-choices like regular excercise.
Actual BDSM can involve this. It's called "predicament bondage" - forced to choose between two or more painful/humiliating options.
Triage during a mass casualty incident can get like this: Do you treat people first-come first-serve, or focus limited resources on possibly-fatal-but-easily-treatable injuries to maximize lives saved, but possibly condemning more seriously-injured patients to an untreated death? In fact triage training comes down to focusing the most effort on the life threatened casualities who are the most likely to live.
During the WWII, Stalin received an ultimatum from the Nazis: either he trades captive Field Marshal Paulus for his captured son Jakov, or Jakov will be painfully executed on camera, and the record will be sent to the father. After a while, Stalin's response was: "I do not trade Lieutenants for Field Marshals". He, however, did whatever he could to save his son via other methods, but all it failed. At least, Jakov's execution was not as horrible as planned - just before it started he assaulted the guards and was shot dead.
There's no conclusive proof that Stalin really said that, although his decision was the same.
Many argue that Truman's decision to drop the atomic bombs was one of these. The alternative would have resulted in likely prolonged war possibly lasting a few more years An invasion of Japan was planned. Estimates put casualties of American, Japanese and civilians in the millions. Given that the USAAF had been laying waste to Japanese cities through conventional means for months at that point, however, its unlikely the choice was too sadistic or even much in doubt for Truman himself.
The Coventry dilemma in WW2 was a classic example, despite that it is an urban myth rather than true. As the British had cracked the German Enigma codes, they knew that the city of Coventry was going to be bombed on a certain night. Instead of warning the city, Churchill let it be attacked to preserve the secret that the German codes were broken. While this specific scenario is untrue the general dilemma of protecting intelligence sources versus using what they are able to give is very much true.
During "introduction" in a prison cell, new inmates might be asked some kind of trick question with a sadistic streak, just to see what they're made of. Usually it will involve a hurtful option and a debasing one, the stock variant being "What'll it be? A fork in the eye or a pork in the ass?" You aren't even supposed to hesitate when chosing the right option, and whether you know that forks aren't allowed in prison cells is secondary.
Cynical types in the American Politics claim the two-party system is essentially this.
A classic question of Utilitarianism: a drunkard is sleeping on a cable car track. A group of people crowds another nearby track. The car is out of control, but you are nearby a switch. The crowd is too thick for all of them to get out of the way, so do you throw the switch and kill the drunk, or let it run over the crowd to save the one? Utilitarianism would say that there's more morality in throwing the switch and letting the drunk die, but neither choice is ideal.
There's also an extension of this question: same situation, but rather than pulling a lever, you have to push the drunk guy onto the track to stop the train from hitting the crowd. Despite the utility value being the same, responses tend to be opposite: those that would pull the lever almost never push the guy.
Rock Center reported on people who had to choose between a pay raise and losing their government assistance because the increase in salary would disqualify them. For example, a single father had to take a pay cut otherwise he couldn't afford daycare for his three young kids.