Many games, especially Role-Playing Games, allow you to recruit characters that have littleor no bearing on the plot. For some games, you can recruit all of these characters if you want.
However, in some games it is not possible to have all playable characters on your team. Maybe recruiting Eve the Elf prevents Dave the Dwarf from joining, or maybe asking that cute cleric to join your cause makes that badass sorcerer leave the party. It could even just be that the heroic knight is found on a different path than the cool pirate chick. Whatever the reason, the game forbids certain characters from being in the party at the same time, requiring you to boot one out in order to get the other or know ahead of time which of the two you want. Sometimes the exclusivity is limited to a single playthrough, and it is possible to use a New Game+ to go back and acquire the other character (ultimately having both). Other times, the game will never allow the two to be together without the use of a cheating device.
Do note that this trope does not apply if you can't recruit a character because the party has a limit on how many members you can have: that trope is Arbitrary Headcount Limit.
In Soul Calibur 3's Chronicles of the Sword mode, there are 2 sets of 2 party members that will join you after defeat at the end of the level, with the first one of the pair that is defeated joining the party. One interesting effect of this is that when a character joins, you unlock their customization items, requiring the mode be beaten at least twice to get all the items.
In the Super Smash Bros. Brawl story mode, one of the first battles has Kirby decide whether to rescue Zelda or Peach from a giant Piranha Plant. The saved character travels with you for the next couple of matches, but eventually, the two story paths merge.
In Castlevania III: Dracula's Curse, when the path forks for a second time, you have the choice of taking the top route (which leads to Sypha Belnades) or the bottom one (which leads to Alucard); they can't meet each other. Furthermore, if you recruited Grant DaNasty during the first fork, you will have to choose between keeping him or taking Sypha/Alucard in his place.
Unless you use the Party Goodie, in which case a spell will allow them to work together.
Chrono Cross, with its Loads and Loads of Characters, has a few examples. Early in the game there are three ways to sneak into Viper Manor, each of which nets you a different party member. Immediately afterwards, you can acquire one of two groups of party members depending on whether you choose to save Kid or not. However, through the use of New Game+, it was possible to get everyone on the team at once.
Siblings Bethany and Carver are mutually exclusive at the beginning of Dragon Age II, and one will be shot down by Schrödinger's Gun. At the end, Anders and Sebastian become mutually exclusive. If you refuse to kill Anders, Sebastian will not only leave the party, but promise to raise an army against Kirkwall.
PC gender determines availability of the Handmaiden or the Disciple.
Light/Dark side meter selects between Mira or Hanharr.
Mass Effect 1 goes for the Player Punch by making you choose between Ashley and Kaidan, your two human squad-mates, on Virmire. "Virmire Survivor" has become an accepted fan term for whoever you pick, as they have similar routes in the rest of the series - chewing you out for working with Cerberus in the second game, then becoming the second human Spectre and (potentially) rejoining you in the third.
The game also inverts this towards the beginning during the Fist quest. You need to recruit Garrus or Wrex in order to find Fist, although you can easily recruit both before confronting him. When you leave the Citadel, if you do not have both characters, the one you don't have will confront you and ask to join your squad. You can decline them, but it is only possible to decline one or the other - not both.
In Mass Effect 2, during Samara's loyalty mission, if your have a high enough Paragon or Renegade score, you can choose to recruit Morinth. However, doing so causes Samara to be killed off, while choosing to help Samara prevents you from recruiting the other character.
In Jade Empire, you are forced to kill either Chai Ka or Ya Zhen early in Chapter 4.
For the penultimate boss battle in Neverwinter Nights 2,Sand or Qara will join the enemy, depending on how high your influence is with the former. If the former stays with you, the latter will not due to their mutual antagonism.
In Mask of the Betrayer, One Of Many can only be created by using Okku's dead body.
The Pokémon series is replete with this trope when it comes to its Mons. Breeding and trading with other players notwithstanding:
There are three elementally-themed starter Pokemon, which you get to pick just one to start your party from.
There is usually a pair of fossils, and you can choose only one to revive into a Pokemon. This is subverted in Emerald Version, where choosing one of the two fossils will cause the Mirage Tower that contains them to sink into the sand with the other, seemingly gone forever. However, after the Elite Four is beaten, one can travel through the Desert Underpass in which the other fossil can be found.
In the first generation (before the introduction of breeding) you could pick either a Hitmonchan or Hitmonlee by defeating the master of Saffron City's fighting dojo. You also received one Eevee which could evolve into only one of three final forms.
In Pokémon X and Y, the Mega-Charizard and Mega-Mewtwo form you can get, as well as several other Mega-Evolution stones, are unique to one of the two versions, with only 1 of each type of stone present per game.
In Radiata Stories, which party members you get depends on whether you side with the humans or the nonhumans.
However that choice doesn't occur until about 2/3rds of the way through the game, before that you can recruit humans and nonhumans alike, though there are many on both sides that remain unrecruitable until after the split, and the allies you recruited of the opposite faction are no longer usable.
Downplayed in Septerra Core, where you can recruit all the possible characters, but if you try to put Selina & Corgan or Led & Lobo in the same party, they'll occasionally shoot at each other instead of the enemy. However you can do a sidequest to befriend them.
Ashton and Opera are mutually exclusive, with Opera requiring the player to trigger a couple of easily missedEvent Flags. Both have quests hinging on a particular dungeon; however, visiting this dungeon is required as part of her recruitment, while for Ashton it's merely a Side Quest. In addition, Opera is required for recruiting Ernst, making him also incapable of traveling in a party with Ashton.
While Precis is easily picked up once you reach her hometown, Bowman will not offer to join if she's in the party.
Leon and Dias are also mutually exclusive, though not because they cancel each other out; Dias will only offer to join if Rena is the main character, while Leon remains a Guest Star Party Member unless Claude is the main character.
In Tales of Symphonia, there is precisely one dungeon during which you can use both Kratos and Zelos at the same time, after which Kratos leaves (again). Later on, there is a way to have Kratos join your team for good, but Zelos will leave the party before Kratos joins.
Prevalent in the Baldur's Gate games. Characters of wildly disparate alignments will sometimes snipe and argue through dialogue at certain points, growing more and more hostile until you're forced to choose which one to keep aboard. Fail to make a choice and combat will break out until one or the other is dead. Fortunately, it's fairly easy to figure out which party members will have this reaction, and you'll often have the option of refusing someone into the party if someone on your team objects.
In Ultima IV, who can or can't join you depends on the class you chose at the start-if you chose a Mage, Mariah the Mage can't join your 8-person gang because it can't have 2 Mages.
In Romancing SaGa, you can't have Albert and Diana at the same time. The two of them are constantly looking for each other, having been seperated during the fall of Isthmus Keep, and short of exploiting a glitch with a very specific set of steps, it's impossible to reunite them in your party.
Playing Jamil's scenario makes it impossible to recruit Farah. She's allowed to be in the same party as Jamil as long as somebody else is the main character; the reason she's barred from joining in his story is because her choosing to wait for him is a critical part of his ending.
In a series which is famous for encouraging you to recruit everyone you can, Suikoden II comes with a few examples. The first is when you are asked to choose between Valeria and Kasumi, both of whom are returning characters from the first game who the player would probably love to have on their side for continuity's sake. Not to mention that they both have storyline connections to other characters you'll recruit (the other two ninja for Kasuminote And Tir McDohl, if you imported save data from the first game, Anita for Valeria), making it particularly annoying that you can't have both. The second comes when you are given two Listening Crystals. These allow you to recruit monsters. You only get the two, and there's four choices of monsters, one of whom isn't even a Star of Destiny.
Just after the halfway point of Suikoden V, you can access a rather difficult bonus dungeon that upon completion nets you the very Mysterious Waif Eresh. If you do not recruit her, then at the very end of the game, you can recruit Euram Barrows to occupy that position in the 108 Stars of Destiny. Eresh has no plot relevance, while recruiting Euram is necessary to complete his character arc...but Eresh is much more useful.
A somewhat unusual example in Legend of Mana: If you complete the Matilda/Irwin arc, you reach a point where you must fight either Daena or Escad with the help of the other. Though you can bring either one along with you for most of the arc up to that point and switch freely, the one you fight is Killed Off for Real and is Lost Forever. (In fact, it's possible for both characters to be Lost Forever, but it will always be at least one of the two.)
In Final Fantasy VIII, it is impossible to have both Odin and Gilgamesh as summonable Guardian Forces. If you get Odin before the end of disc 3, he is replaced by Gilgamesh during the battle against Seifer. If you wait until disc 4 to get Odin, Gilgamesh is lost. Gilgamesh is arguably more useful since he can cause damage even to enemies that are immune to instant death, but he's unreliable since you have no control over which of his 4 swords he'll use...one of them being a Joke Weapon that does only 1 HP worth of damage.
If you choose Cyuss, you can't recruit Ashlay, and vice versa. In the remake, recruiting Cyuss also means you can't recruit Erys.
Recruiting either Cyuss or Ashlay means that Phia is not recruitable in the early game outside of serving as a Guest Star Party Member, though you can still get her later permanently if you have six or less characters.
In the remake, if you recruit Erys, you will lose Mavelle. Justified, as Mavelle is Erys, just in another body. She'll reclaim her original body if you recruit her.
In Etrian Odyssey III, roughly halfway through the game you're forced to choose one of the two endgame paths, influencing (among other things) which of the game's two unlockable classes you earn after defeating the next boss. If you sided with Armoroad, you unlock the Shogun, while if you sided with the Deep City, you unlock the Yggdroid. Fortunately, they stay unlocked on a New Game+, which means you can ultimately have both classes in the same party.
In Soul Hackers, summoning demons into your party shifts the total party alignment, limiting what other demons you can add. So if you have two Chaotic demons out, you won't be able to summon a Lawful one. The DS Updated Re-release comes with an option to turn this off.
In Chapter 13 of Mystery of the Emblem, there are two villages that are right next to each other. One contains Samson, a fairly powerful Hero, while another contains Arran, a Crutch Character Paladin. If you send Marth down to those villages and enter one, you can recruit one of them. However, doing so causes the other village to close its gates, prevents you from getting the other character.
Halfway through Chapter 3 in Gaiden there are two bosses, Sonia and Deen, that each control their own armies and both block different routes to another boss, Geyse. After fighting and killing one of the bosses, the other will retreat and can be recruited later, after you defeat Geyse.
In Chapter 6 of Genealogy of the Holy War, you can recruit either Johan or Johalva, but doing so enrages the other one and makes them unable to be recruited.
There's also something of a long-term case in regards to the children characters and their replacements; in the first generation of the game, you could pair up certain characters and have them marry. If you did this, the second generation would consist of children of the characters from the first generation, barring certain exceptions. If you didn't do this, you'd instead get a set of "replacement characters" who for the most part were unrelated to characters from the first generation. While it is possible to have some sets be children and others be replacements, it is obviously impossible to have the replacements meet the children they're replacing (even though the replacements exist even if they're not in your party; one of them is even the cousin of one of the "main" children). Of course, most of the replacements were inferior to the children in terms of stats, usable items, and skills, so it wasn't much of an issue.
In Thracia 776, recruiting Eyrios requires you to have not recruited Olwen a few chapters before, and recruiting Sety causes Cyas to leave the party.
Branching paths make it impossible to recruit Bartre and Echidna in the same playthrough of Sealed Sword, and a second branching path will prevent you from getting either Yuuno or Dayan. Likewise, you can't re-recruit Wallace in Blazing Sword without giving up the opportunity to get Geitz.
Also in Blazing Sword, certain actions you take in the chapter "Pale Flower of Darkness" determine whether Harken or Karel will appear.
In Path of Radiance, there is a Duel Boss against the Black Knight. If you fail to win but survive for five turns, Ena joins the party. If you beat the boss, Nasir joins instead. Then, during the final level, you are given the option to recruit between one of three powerful new characters. However, once you've picked one, the other two are unavailable for the rest of the game.
In Shadow Dragon, doing the sidequest to recruit Nagi both requires Tiki to have died earlier in the game and also prevents Gotoh from joining the party. (and while Elice can bring Tiki Back from the Dead, it's impossible to recruit Gotoh no matter what you do.)
Shadow Dragon has several other examples, in that you can only access certain sidequests by having a maximum of 15 living units at the time. This is doable if you spare only the characters you use most frequently, but many players have issues with letting even one of their party die.
Jagged Alliance: Some mercs will refuse to work with others, either turning down your offer on the ground that you have their personal enemy or leaving the party. Though this feeling is not always mutual, so hiring people in right order you can sometimes hire both of them.
In the first game, failing to listen to the complaints of your mercs can have terrible consequences: Fidel does not like working with Hurl, for example, and failing to fire one or the other will result in Hurl disappearing in the middle of the night (the implication is that Fidel killed him), and you'll lose all Hurl's equipment.
In the second game, if you manage to hire two mercs that do not like each other, they will (grudgingly) work together for the duration of their contracts. However, when the option to renew their contracts comes up, both of them will refuse to extend their contracts, meaning you'll lose two mercs instead of just one.
In Shining Force 2, when you go to Creed's Mansion, you are given a choice between four characters: Karna, Tyrin, Randalf, and Eric. After you pick one, the other three become unavailable to you. Subverted, in that later in the game, it's possible to recruit the characters you missed.
In Tactics Ogre: Knight Of Lodis, the player can, at a certain point in the game, decide between two paths. On one path you recruit Shiven and Cybil, while the second path has you recruit Orson and Rictor. Then, later in the game on both paths, you are given the option to recruit either an Angel Knight or a Lesser Daemon, which locks the other from you, but if one of them dies or be turned into Infinity+1 Sword you can still do the event of getting another (only if you didn't complete Lesser Daemon event with alive Angel in your party).
In the original Tactics Ogre, the path you take will determine which party member you will get:
Choosing the Law route will let you re-recruit Vyce, and also gives you the option to recruit Xapan, Jeunan and Ocionne the Dragon Tamer. The PSP remake also includes Ravness and Ozma as your exclusive characters in your party.
Choosing the Chaos route will let you recruit Arycelle the Archer (although in the PSP remake she can be recruited in the Law route), Folcurt, Bayin and allows you to complete the Four Phoraena Sisters roster as it lets you recruit Cistina and Cerya.
Stay in the Chaos route and in the original version, you get to keep Arycelle, and in the PSP version you can recruit Cressida.
Move to the Neutral route and you can recruit Oelias and Dievold. However, Gildas, who's available in every other routes, is unavailable here, while in the original version, Arycelle leaves your team.
In Odium, if you go into an optional side-area to recruit Slavsky, one of your teammates, Medusa, goes insane first and must be killed. Technically, that's also Arbitrary Headcount Limit in play, since having both Medusa and Slavsky would exceed your limit of 5 members.
In Yggdra Union, you recruit either Roswell or Rosary after killing one of them. The survivor joins your army.
In Blaze Union, your final party member is determined by Road Cone—Baldus in route A, Emilia in route B, and Baretreenu in route C.
Similarly, in Gloria Union your REP value determines whether you get Yggdra or Gangr in Chapter 4, and whether Eater or Pamela is available in Chapter 5.
In Shin Super Robot Wars (during Scenario 28 of the Earth Route) Domon Kasshu wants to settle the score with Allenby in a Gundam Fight, but Rain doesn't really buy it and storms off. Domon can then choose to go to fight Allenby or to go after Rain. If you choose the former, you have done a step to get Allenby and her Nobel Gundam, but if you do the latter you can get a chance at Rain in the Rising Gundam. Also, in the same game (and any game with Blue Comet SPT Layzner as one of the series), you eventually get the choice for Layzner's Mid-Season Upgrade: The Powered Layzner or the Layzner Mk 2 depending on how you handle a mission earlier, though that's more a Mutually Exclusive Power Up.
If Gendo chooses to activate EVA-03 in Super Robot Wars Z3: Jigoku-Hen, Z-Blue loses Asuka and gets Mari for the rest of the game.
Real Time Strategy
Majesty does this with unit types, specifically the non-human races, and the various temples and their priests. If you recruit one of the non-human races, you can't get the others unless the mission starts you with more than one of them already (elves think dwarves are uncouth, dwarves think elves are snooty and corrupt, and both look down on the gnomes). Also, while there are numerous gods, some hate each other so building the temple of one will lock out two or three others - or in the case of the barbarian war god, all of the others. Then again, the barbarian god's "priests" and only spell are so powerful it's sometimes very worth it.
Age of Mythology and its expansion have this in terms of gods. Each individual faction has three starting gods as benefactors, and every time your population advances in age (level), you have to choose between two different gods to advance you each time. For example, when you begin a skirmish in the Archaic Age, if you play the Greek army, you start with either Zeus, Poseidon or Hades as your benefactor, and if you choose Poseidon, when you advance to the Classical Age, you have to choose between Hermes and Ares as benefactors. Given each individual god has their own unique God Power, unique unit upgrades, and unique Myth unit, very often you will have to choose between having one particular legendary creature in your army while excluding the other.