Used in Zork Zero. You're faced with being executed, along with several other people, and everyone gets to make a last request. If the executioner can do it, he hangs you. If he can't do it, he beheads you. When it's your turn, the correct request is "behead me." So he'd have to cut your head off, then hang you. But he's only supposed to cut your head off if he can't do it, and you wouldn't have a head or neck anymore to be hanged from... The executioner eventually gets upset and has you tossed out.
And yes, if you go back in, the executioner has come up with a third execution method just for wiseacres like you.
In The Curse of Monkey Island, Guybrush Threepwood is asked, while challenging a pirate to a duel, to "Choose your weapon," and is presented with a case full of pistols. No matter the weapon he chooses, he loses the duel. If the player closes the case, a banjo is revealed to be behind it. The correct option is to choose duelling with banjos.
Doubly played with, in fact, as the pirate proves to be an exceptional banjoist. Instead of admitting defeat or being an even better player, Guybrush has to defeat him by picking up one of the aforementioned pistols and shooting the banjo, thus proving himself to be sneaky and dishonourable enough to be a pirate captain.
In Myst, you're presented at the start with brothers Sirrus and Achenar trapped in books, each accusing the other of destroying their father's books and being wrongfully imprisoned by said father. Additionally, Achenar claims that Sirrus killed their father, while Sirrus says that father went on a journey to discover the truth and was never seen again. Throughout the game, you collect pages that allow you to hear more of the brothers' stories (while finding virtually no evidence that would support either of them). In the end, you're confronted with the choice between freeing Sirrus or Achenar. The correct answer: They were both in on it, and you shouldn't free either or you'll be trapped yourself. Instead, you have to use the green book which both brothers warned you against, freeing their father to destroy the red and blue books. Oh, and make sure you take the right third option, i.e. get the white page before using the green book.
The whole series has many problems like this (as well as many puzzles in which you just have to solve it the long way). For example, in Riven, Gehn gives you the option of using the Trap Book (which he thinks is a Linking Book that will take him home), or of refusing, which will get you killed if you do it too many times. The solution is to voluntarily use the book and trap yourself, which will convince Gehn to use it as well, thereby taking your place in the Trap and freeing you.)
Myst 3: Exile offers such a dilemma. Once you've activated both of the crystal podiums in Narayan, Saavedro will approach you and, realizing that the Narayan society is still alive and well and that he can't go home without you turning the outer shield off once he's on the plaform, will tell you to release the outer crystal and will walk out. Refuse and he'll eventually kill you. Do as he asks, and he'll gllefully toss the Releeshahn book into the drink and ride off, leaving you to go back to Atrus empty-handed. The best answer? turn off the power, trapping Saavedro between the crystals. If you approach the window after doing it, he'll give you the Releeshahn book and will plead for you not to leave him trapped. This leads to yet another of the same type of dilemma. If you leave him, Atrus will comment on the cruelty of that act, but if you turn the power back on, lowering the inner crystal, he'll charge back in and kill you. The answer this time is to turn the switch lever and then restore power, releasing the outer crystal and allowing Saavedro to return to his home without ever exposing yourself to him.
In Myst 4: Revelation, you're confronted with Yeesha strapped to a chair, asking to be freed by pulling a silver-colored lever. Her brother Achenar is also in the room, and claims that Yeesha is actually Sirrus, his brother, transferred into her body, and demands that you pull the amber-colored lever instead. Taking a third option by refusing to act is not the correct solution in this case (subverting the trope); in fact, this is one of two ways to get a bad ending (the other one is pulling the silver lever). The correct choice is to trust Achenar and pull the amber lever, which transfers Sirrus out of Yeesha's body.
Finally, in Myst 5: End of Ages, the player is constantly running into Yeesha and Escher, who each cajole you in different ways to give the Tablet to them, but who are each unworthy to have it for different reasons. The answer is to put the Tablet on the ground, so that it can be picked up by the Bahro, who were its rightful owners originally.
In Knights of the Old Republic, there is a quest of sorts presented to you on Dantooine by a Twi'lek jedi named Bolook, who is investigating a recent murder. The two suspects, Rickard Lusoff and Handon Guld, must be questioned in order to determine which one actually killed the victim, a farmer named Calder, in addition to corroborating evidence with an information droid. After 4 rounds of questioning, and calling both parties on false testimony and possible motives, you find that they were both guilty, and that Calder was sleeping with Handon's wife and had a business deal with Rickard which went sour. This gets you the more than double the XP of just naming one murderer.Full Details
Legacy of Kain: Soul Reaver 2 sees (and deals with the results) of this exchange:
Raziel: You said it yourself, Kain - there are only two sides to your coin. Kain: Apparently so. But suppose you throw a coin enough times... suppose one day, it lands on its edge.
The above was due to a choice Kain had to make. If he killed himself, it would seemingly restore the pillars of Nosgoth, but that would finish off the vampires. If he didn't kill himself, then the vampires would remain due to his presence, but Nosgoth would remain. At first it seems he chose option two out of a desire to survive. It turns out that the entire situation was crafted carefully by Moebius and his Elder God. If he killed himself, Nosgoth would be doomed anyway because the vampires kept the pillars preserved. He actually took a third option. In a convoluted (but awesome) scenario he purified himself so he could fulfill his destiny as the Scion of Balance, making the pillars unnecessary.
Soul Reaver is one big quest for that 3rd option which will satisfy everyone who hated the end choices from Blood Omen: Save the world but sacrifice yourself, or rule over a crumbling Nosgoth.
In Mass Effect 2, Tali's loyalty mission involves being her being accused of treason. While investigating a quarian science ship, Shepard finds evidence that Tali's father was conducting dangerous experiments on the geth. Shepard can choose not to tell the quarians about this, which is what Tali wants. This results in Tali's exile, but earns her loyalty. Shepard can also reveal the evidence, which gets Tali acquitted but loses her loyalty. Or Shepard can call out the quarian admirals for their politicking and shame them into acquitting Tali while still earning her loyalty.
There's actually a fourth option here, or a second third option, as it were. You can convince the other quarians you've encountered to stand up for Tali to the Admiralty Board, which has the same result as doing it yourself, but doesn't require the high Paragon/Renegade score that the first one does (and is a Moment Of Awesome for them). You do have to make sure that they're alive and sane, though, and that's far from given.
The entire Mass Effect series is full of these, in the form of Charm/Intimidate checks. Most of them are "third options" that both do roughly the same things despite being tied to different karma, and that typically solve whatever problem needs to be solved without any trouble. This is why charisma is a good thing.
A Good Example is in Lair of the Shadow Broker, Tela Vasir is holding a random woman hostage, the normal options are to do as she says and drop all your ammo, shoot through the woman, or (with sufficiently high Paragon or Renegade) give either a Badass Boast or a "The Reason You Suck" Speech while Liara hits her with a table.
At the end of Priority: Rannoch in Mass Effect 3, Legion (or the Geth VI if Legion died in Mass Effect 2) tries to upload the Reaper upgrades into the geth, upon their freedom from the Reapers. However, the quarian fleet is still hellbent on obliterating the upgraded geth, causing it to be the one to be wiped out, instead. It's at that point, Shepard has to either continue the upload at the expense of destroying the quarians, or kill Legion so that the quarians can destroy their creations without getting wiped out themselves.
The third option: use a reputation check to convince the quarians to stand down and allow the geth upload, which results in the two sides making peace and allying with the Alliance against the Reapers. This Golden Path has extremely steep requirements, only available if Shepard has at least four bars of Reputation, imported a Mass Effect 2 save where both Tali and Legion were recruited and survived, completed "Rannoch: Geth Fighter Squadrons," and did at least 5 points' worth of the following: destroyed the heretic geth in "Legion: A House Divided" (2 points), completed "Tali: Treason" by using a reputation check to get Tali acquitted without giving evidence of her father's treason (2 points), brokered an agreement between Tali and Legion in their argument (1 point), and completed "Rannoch: Admiral Koris" (1 point) by rescuing the admiral instead of his crew (1 point, separate from the other).
The ending of the third game plays out this way. There's two regular options that are suggested by Admiral Anderson and the Illusive Man respectively, destroying all the Reapers (and all synthetics by extension) or controlling the Reapers and ordering them to leave. However, if your Effective Military Strength score is high enough, the Catalyst provides a third option of combining synthetics and organics, ending the cycle of synthetics vs. organics. As of June 26, 2012, the Extended Cut adds a fourth option. killing off everyone in the galaxy. However, the after-credits scene indicates that The next cycle was able to defeat the Reapers using the information in Liara's beacons.
Played straight in Neverwinter Nights. When you reach the village of Charwood, you are told to affix the blame for a centuries-old massacre. It turns out that the murderer was neither of the adversaries responsible for half the events, but rather the demon that was manipulating them both. On the other hand, exposing the demon leaves you in another dilemma; you can either let a demon lord go free and bag yourself a magical trinket, or doom a town of people to eternity in amnesia and madness in order to trap the balor. Great, huh?
Even after revealing the demon lord you can still decide if one off the former suspects is guilty. One of the suspects could have chosen not to execute the massacre and abandoning his plan with eternal undead. The overall outcome is more positive.
An infamous moment in video game history, in Final Fantasy VIII: when you are trying to acquire the Guardian Force Bahamut, you are asked several questions to test your character. The worst gag is the answer to the third question is an invisible third answer, which is only seen when you've decided on it.
The third option is a big plot point in Final Fantasy X: Between letting Sin continue it's endless rampage against Spira and sacrificing Yuna (and probably Tidus as well) in order to destroy it, only for it to inevitably come back anyway. The third option in this case was to take advantage of Sin's (i.e. Jecht's) weakness to the Hymn of the Fayth, then use the airship to get inside it, destroy it (him) from the inside, and use regular aeons and good old-fashioned beatdown to destroy Yu Yevon (who created and controlled Sin) before he could recover. This was probably Auron's plan to begin with; he probably just let Tidus and the others figure it out on their own.
Final Fantasy Tactics sort of has one. Near the end of Chapter One, Tietra - the sister of Delita, Ramza's best friend - is taken hostage by the Corpse Brigade (long story short, they mistook her for a noble along with Alma, her best friend and Ramza's own sister, and she was the one unlucky enough to be abducted successfully). The kidnapper, Golgorath, holds a knife to her throat when Zalbaag and his forces catch up, and threatens a choice - let him go free and live, or he'll kill her. He's actually hoping for the former, but is willing to spite them. As Ramza and Delita arrive, Zalbaag makes a horrific Third Option: order Argath to Shoot the Hostage instead and then Golgorath afterwards. Technically speaking this resembles Option #2, but with a twist - Zalbaag is refusing to comply with either alternative and would rather not let a rebellious criminal (albeit one with sympathetic motives) dictate his options. Ramza does call him out on this much later in the plot, too.
In Deus Ex early on in the game you are instructed by your CO to kill the unarmed leader of a group of terrorist/freedom fighters who has already surrendered or else she will kill him for you and report you for insubordination (which she will do if you try to leave or even so much as talk to him for too long). An unsaid, but also perfectly viable option, is to just kill her instead, and claim she got killed in the crossfire. It is difficult to do without killing the terrorist leader anyway because your CO explodes when you kill her.
It's possible: when you enter the terrorist's bedroom, put a LAM or two on the wall. After the first chunk of dialogue, when you hear Anna Navarre's footsteps, run to the bathroom, so you won't die too. When she's blown up, you can continue your conversation with Lebedev - it's worth it, for he has some crucial and interesting information.
Or you can take the fourth option, try for a non-lethal kill. It's impossible to actually knock out your CO, but you can do sufficient damage to cause her to run from you without landing the killing blow. Your still be forced to kill your CO later in the game to move forward. Unless you take the third option again via sequence breaking. The game never adequately explains why your bosses seem to be unaware that you attacked your CO despite her being alive and perfectly capable of reporting the incident.
The Deus Ex: Human Revolution DLC "The Missing Link" confronts the player with a choice - poison gas is flooding the facility, and the protagonist can divert the gas to one of two areas, saving either hundreds of innocent people, or a whistleblower who is prepared to blow the horrific practices going on in the facility wide open. Finding and disabling the well-hidden pump for the gas nets the player high praise from some support characters and an achievement named "all of the above".
Aigis of Persona 3 FES has to make a tough choice - leave behind the memories of the person she loved, or go back in time to save him (which would doom humanity or get them stuck in their dormitory forever). Instead she decides to find out how exactly the Main Character performed his miracle and if there's a way to save him using the last remaining Door of Time, which allows them to use the Key of Time for something else, like leaving the dorm.
Another one takes place in Virion and Olivia's supports. He's teaching her some new dances but one of them is a duet, and she's too shy to go through it. Will Virion step on Olivia's boundaries so she'll learn new dancing steps, or wil he stop the classes altogether/leave that particular one unfinished? He decides to go to the other side of the place they're both in and mimic the steps from that corner, so she can see the basics and learn them without problem.
In the final puzzle of Star Trek: A Final Unity, Picard is forced to choose between using a superweapon to annihilate a Borg Fleet, or simply using it to nonviolently halt their invasion. Naturally, the correct choice is None of the Above.
About all the solutions in Star Trek: Borg are almost never either the two choices given to you, but an absolutely insane third option that nobody would try on their first time. Thankfully Q gives you lots of tries...
In Kingdom Hearts: Chain of Memories, after playing through the game as Riku, Riku meets up with King Mickey, who suggests that he keep his dark powers, saying something to the effect of, "You chose a road I never even thought of; I want to see where that road leads." Later, when asked whether he'll take the road to light or the one to darkness, he takes the one in the middle... "the road to dawn."
In Mario & Luigi: Partners in Time, when the titular Bros. try to access the Star Shrine, the Sprite gives a test of purity. Examining Mario's spirit, the Sprite determines that he is pure enough (and mildly overweight, at that), but Luigi's past is dark enough (illiciting some horrified mutterings from the Sprite) to bar him from entering, and he must hit a special block in order to get in. After completing the puzzle to get the block to the door, Luigi is unable to hit it, and the Sprite asks who was responsible, giving you three choices: 1) Mario, 2) The Babies, 3) Luigi the correct answer is 4). After taking the test, the Sprite is dissatisfied with Luigi's dishonesty and agrees to only let Mario and the babies in, ignoring the point-out that he only gave three answers, none of which were correct. Mario debates on Luigi's behalf to the outraged Sprite, and his selflessness is apparently strong enough for both of them. He then reveals that the whole event was a test in and of itself, and they passed with flying colours.
Geneforge 4 has you start off allied with rebels who will kill thousands to overthrow the government, but will let you defect to the other side, which will smash the rebellion and reinstate oppression and servitude. Both refer with distaste to some group known as the "Trakovites," which they're doing their best to stamp out...
The Mega-Ten Series has this Trope as a major theme, as the main character has the choice of aligning yourself with Law(Usually represented by the Messians who worship YHWH, a vain dictator who created the world to be his) or Chaos (Usually represented by the Gaians, who think that it's every man for himself, and are usually aided by Lucifer). Neither is the right option however as the Law path has no liberty while the Chaos path results in self destruction. The (arguably) correct path is Balance which supports personal liberties and individuality while not falling in a state of anarchy. Again this is arguable since the games allow you to choose whichever path you want and treat you as the victor no matter which you chose.
Somewhat of an aversion as well. Broken Steel gives you more options, but every option you have is non-canon, since Broken Steel retcons the ending to explain why the Lone Wanderer and Sarah are both incapacitated, but neither is dead.
In Kingdom Hearts II, the villain Xaldin of Organization XIII has the Beast caught between a Sadistic Choice. He has stolen the Beast's rose, as well as Belle. However, he will let one of them go, at Beast's choice. And there's not a damn thing Beast can do about it. Belle, on the other hand, catches Xaldin off guard by elbowing him in the side, takes the rose, and runs. Even Sora notes that as Belle's running, she seemed to be having a really good time.
Twisted Metal: Head-On has one of these in Agent Shepard's ending. The winner of the Twisted Metal Car Fu tournament gets a wish from Literal GenieBig Bad Calypso; typically they get screwed over. Rather than fall for this, Shep decides to just arrest Calypso.
The best part of which is Flipping the Bird to members of the third potential faction (after having killed the other two) as you walk off into the night.
Grand Theft Auto: Vice City exemplifies the whole concept of sufficiently advanced video games allowing a third option. One mission has you chasing a crazed stalker. The official game guide suggests ramming his car until it explodes or doing a drive-by. It's possible to steal enough cars to create a roadblock and then use the rocket launcher. This is just one of dozens of examples.
For a Rogue-alike, ADOM has an unusual amount of plot, and there are several Third Options available in the game. If you take the quest to look for the village carpenter, you'll find he's become a dangerous Chaos monster, who will attack you on sight. It's kill or be killed ... or you can lead him to the healer Jharod, who will fix his corruption and teach you the Healing skill as a reward. Later on, you'll meet an undead dwarven warrior, who can be defeated by force, or destroyed instantly by pouring holy water on his grave. Later still, you'll run into a dying sage who can't be healed by any normal spells, but he won't move off the stairs to the next level until you talk to him, at which point he dies. The third option is to give him an amulet of life saving. When it comes to the endgame, you can close the Chaos gate and kill all the monsters on the level, preventing it from being reopened ... or destroy the levers so the gate can't be reopened ... but if you've done a variety of difficult tasks, you can go through the gate instead and fight the god of Chaos for a special ending.
In Wing Commander III, at one point you're given a choice between kissing Rachel or Flint, which would make the one not chosen mad at you (and thus unavailable, leaving you to either fly short a wingman or configure your own ship loadout if you don't want to launch without missiles, respectively). However, you can choose to not kiss either of them, by bypassing the decision scene entirely, and have both still available. Both will be unhappy with you and their morale will take a small ding, but only for Flint does that really matter, as lowered morale makes her flying less effective.
The beginning of the fourth game, in which Commander Blair is drawn out of a quiet and lonely retirement, strongly hints that this is actually canon.
Dragon Age: Origins gives you a third option at Castle Redcliffe, where the Arl's son Connor has been possessed by a desire demon, torturing the castle denizens and wreaking havoc on the village with frequent attacks from the undead. At first the choices are to kill Connor or sacrifice his mother, Arlessa Isolde, in order for a mage to enter the Fade and slay the demon. But, if you ask about an alternative, you'll be presented with the option of having the mages of the Circle Tower assist in the ritual, sparing both. If you are a mage and choose to enter the Fade yourself, you're also presented with a fourth option by the desire demon herself: Allow her to leave, temporarily relinquishing control over the boy, in exchange for a reward of your choosing.
In the Dalish Elf quest, by the time you encounter the Lady of the Forest, she explains that the werewolves she protected were once humans, before the Dalish Keeper Zathrien turned them into werewolves, all as an act of revenge for his dead children. It's at that point that the player can either kill the werewolves and quench Zathrien's thirst for revenge, side with the werewolves and help them pay back the elves for their curse, or, as the ultimate third option, sacrifice Zathrien and the Lady of the Forest's lives to return the werewolves back into humans.
By the end of The Landsmeet quest, the Warden protagonist is given the option of killing the traitor, Teryn Loghain, or turning him into a Grey Warden while replacing Alistair with the teryn. He/she also has to decide whether Alistair or Anora becomes the new ruler of Ferelden. If Loghain is spared, Alistair can't be chosen to lead Ferelden. If Loghain dies, Alistair is a feasible choice for ruler of Ferelden.
Thankfully, there is still a way to elect both Alistair and Anora as the new rulers of Ferelden, while Teryn Loghain lives and becomes a Grey Warden. First the player has to harden Alistair after the events of his own side-quest, so that he could be more willing to become king. After that, the player has to persuade Alistair and Anora to marry each other, so that both can rule Ferelden together, while Loghain lives.
As a fourth option, if the protagonist is a human-noble, he/she can either marry Alistair if female, or Anora if male. Regardless of whom he/she marries, he/she becomes a ruler of Ferelden him/herself.
The ending also provides a third option. Instead of sacrificing yourself, or a comrade warden, to the Archdemon, you can have Morrigan impregnated, either by a male PC, or Alistair or Loghain. Doing this lets the Archdemon's essence join with the unborn child.
There's a fourth option, instead of giving Morrigan a god-fetus, or sacrificing yourself or Alistair. When you take down Teyrn Loghain at the Joining, you can opt to recruit him for the Grey Wardens, and make him finish off the Archdemon.
Dragon Age II also subverts the idea that the third option has to be an optimal outcome in the quest Night Terrors. A boy with a rare magical talent is being threatened by demons. The choices first given to you are to either save him and let him run away to train his talents or to make him Tranquil (essentially a magical lobotomy). The third option is to let another demon posess his body, wreaking havoc with the boy's magical talent in exchange for a reward from the demon.
In Fable III, after taking the throne, you discover why your brother Logan was such a terrible ruler, and you are faced with the same choice: either keep your promises to those to whom you have made them, thereby dooming Albion to the demonic presence looming on the horizon, or break your promises, gaining you enough funds with which to defend Albion from said evil. It's quite possible, though, for you to simply buy up all the property in the game, which eventually deposits enough money in the royal treasury for you to build up your defenses while keeping the moral high ground.
There's also an inversion in the early game where Logan forces you to choose between killing a group of protesting commoners and killing your childhood friend/lover. If you take too long to make this choice, he orders all of them to be executed.
If you start looking into the Dark Brotherhood in The Elder Scrolls V: Skyrim, you'll find yourself waking up in a locked shack, where the Brotherhood's chief assassin explains that you owe her group one murder. She has three bound and hooded victims waiting for you - a harridan of a housewife, a blubbering Nord mercenary, and a Kajiit who unrepentantly mentions that he's a rapist and murderer - and explains that there's a contract on one of them. Someonehas to die before you leave the shack. Kill one and the assassin will welcome you as an initiate in the Dark Brotherhood. Kill more than one and she'll praise you for your thoroughness. Or... you can kill the assassin (no easy feat), free the captives, and report to a city guard, starting the "Destroy the Dark Brotherhood" quest in which you assault the assassins' lair and wipe them out for good. This is an improvement from Oblivion, where you could only opt in or out of the Brotherhood without doing anything else.
In the end of the first Dino Crisis, Regina must choose between helping a mortally wounded Gail (Regina's commanding officer) apprehend the renegade scientist Dr. Kirk, causing Gail to die in the process; or knock Gail out, forcing him to escape the island without capturing Dr. Kirk. The third option comes when the player chooses to knock out Gail, only to go after Dr. Kirk alone.
Meta-example: The series is famous for its Alternate Timeline, but the older 2D games don't really fit anywhere on it. Instead of making a game to connect them to more recent entries, Nintendo opted to create a third branch in which Link died during Ocarina of Time. Like Skyward Sword, it gained as many detractors as defenders.
In the MMORPG PlaneShift getting killed sends you to the Death Realm, which you have to explore to find the portal leading back to the mortal coil. Your first choice comes when the bridge you're on branches. Right or left? Both paths are dead ends, just keep going straight ahead and drop off the bridge.
In Jade Empire, instead of (Good Ending) healing the water dragon or (Evil Ending) claiming her power for yourself, you can sacrifice yourself and let Master Li win. Your reward for allowing his evil dictatorship? A statue of yourself. Derp.
In the fifth chapter of Strong Bad's Cool Game for Attractive People, Strong Bad needs some tech support. Unfortunately, the guy on the phone isn't interested in helping and tries to impersonate a voicemail system with multiple responses if Strong Bad says "One," "Two," or "Three." None of the responses are helpful to the player; the way to proceed is for Strong Bad to take a fourth option and say, "Four." This causes the tech support guy to panic and concede defeat.
In the extensive Baldur's Gate NPC mod, there are three romantic suitors for a female PC. Two of them, a knight and a rogue, will go through a series of impressive challenges in the hope of winning the PC's heart, which may well make it very difficult to decide between the two. Since the third opts out due to thinking his chances are hopeless, this makes him an endearing and tempting third option (as evidenced by polls, wherein he is the single most popular choice of either gender.)
Early on in Baldur's Gate II, the PC is given a (theoretical) moral quandry similar to Morton's Fork, involving the PC and his (imaginary) sister being trapped in cages by a wizard and each having to choose whether to try to save themselves or their sibling in a variant on the prisoner's dilemma. If Minsc is in the party, he interjects by saying that he would smash open the cage and attack the wizard for playing such a trick.
Shin Megami Tensei: Strange Journey presents you with a dilemma in Grus. A demon has sealed the path to Maya, the area's boss, and demands that you kill the newly-pacified Jack's Squad before he'll let you through. However, the newly-angelic Zelenin offers you another option: use her song to brainwash the demons and make them open the path. Killing Jack's Squad is the Chaos option, while using Zelenin's song is the Law option. There is, however, an unpresented Neutral third option: Kill the demon that's sealing the path in the first place.
A third example in the undersea area: A turf war is being fought between two gangs of fish obsessed with sport: the Ice Skates and the Roller Skates. You can help one side against the other, or help a third faction, the Skate Board, drive both away.
In Fallout: New Vegas, rather than just choosing to side with the NCR or Caesar's Legion, the Courier is given the choice to secure Vegas under the rule of Mr. House. You can even go one step further and decide to screw them all in order to make Vegas an Independent city-state under your own rule with the help of the Yes-Man A.I. Additionally, in many more minor choices the player has to make they can sometimes, if they have enough of the right skill, choose an extra option (it's also there when they don't have the skill, but it has no effect and both the player's words and the response are generally Played for Laughs) that will reward them with a sense of satisfaction, some amusing or badass dialogue and will often allow them to skip an annoying resource-gathering quest or give them the advantage of free or cheaper weapons, armour or supplies.
There is one case where not having enough skill but still choosing the skill-option opens up a new option: in the final battle against Lanius, if you fail the final skill check in the chain to convince him to retreat, a less hard speech check becomes available: talking him into fighting you one-on-one.
In Monster Girl Quest at one point you're given the option to either touch a kitsune's fluffy tail or have some of her fried tofu. Both choices lead to bad ends, since she takes away a magical artifact you need to continue. The third option is to ask her to hand over the artifact. Not a huge surprise, since all three options are listed from the start. But if you take the wrong option on purpose, you get scolded by Alice and Luka is surprised that there was a third option.
In Duel Savior Destiny the Messiah upon ascending to their position is forced to choose between the Red Law (magic) and the White Law (science) to determine which will be the new natural law in the new universe. Taiga, who recognizes that both of them are necessary, chooses instead to beat up God and make him stop offering such shitty choices since they destroy the current universe.
The entire plot of Tales of Symphonia revolves around the protagonists' efforts to Save Both Worlds despite their condition of being in a hourglass-like state where life-giving mana must flourish in one and decline in the other - there isn't enough for both. And the whole process starts with the hero refusing to sacrifice The Chosen One in order to save his own world, insisting that he'll find a way to save both of them and the other world as well. He does, but it's sure not easy.
One was taken by Sougetsu Kazama in Samurai Shodown III. Faking your rebellious little brother Kazuki's death so he and your sister Hazuki can run away is way more useful than either letting him go and being marked as a failure by your clan, or killing him and definitely losing both of your siblings.
Spec Ops: The Line uses this as an actual game mechanic in places. The game will offer two (horrible) choices to the player, but will acknowledge other actions as answers without explicitly stating them. For example, the player comes upon a man accused of stealing water and a soldier who used unnecessary force against him, both of whom were sentences to death and are hanging from nooses. The player is asked to choose which of them is guiltier. Snipers just ahead will shoot out the rope of the one the player doesn't condemn—or shoot at the player if he refuses to choose. In addition to the options of shooting either man or doing nothing, shooting at the snipers or shooting the ropes themselves are also considered valid responses.
When you examine the Magicant machine in The Halloween Hack, you are given two choices: "Kill the monster" and the text box border (which the game tells you to pick a "real answer"). To see the rest of the game, you must refuse by pressing the B-button.
At the climax of Grand Theft Auto V Franklin is offered two options: kill his friend Michael for Merryweather Security owner Devin Weston, or kill his friend Trevor for high level FIB agent Steve Haines. Weston refers to defying both of them as "Option C" and a death wish. If you choose "Option C", Franklin, Michael, and Trevor take out Steve, Devin, the leader of the Triads that's been harassing them, and Stretch, the guy that has been getting Franklin's friend Lamar into trouble, for good measure.
Franklin: Hey, my bad, homie. I picked "C". Ain't that a bitch?
Getting the best endings of all three games in the Ar tonelico trilogy boil down to this as the main heroes are constantly getting pulled into the actions between two major factions that are trying to save/change the world their own way (and have to be helped/stopped at one point or another) but, in the end, find their own solution that benefits everyone in the end.
Antichamber: Many of the puzzles will have this as a solution. Early on there is a hall leading to two stairways, one going up and one going down. It doesn't matter which one you take, they both lead back to right in front of both stairways, the solution is to turn around and go back down the hallway you came.
Not doing anything during the "Live Selection" sequences of Resident Evil 3: Nemesis was a third potential choice along with the two given. If monsters were involved it would simply leave you to your devices to kill them, but in other cases sometimes an entirely different outcome rather than the two choices would happen. Including a third potential ending sequence.