You pick your favorite character in the character select screen. Then you play the game and lose. Let's try it again. No dice, you lose again. And this keeps happening until you change to another character, who creams the level, without being the Game Breaker. Usually, this didn't even look like a job for Aquaman.
What happened was that the game designers wanted to encourage players to try out the more obscure characters, abilities or techniques. Sometimes, the level design suggests that much, when it should be set up with the general mechanics and bigger potential issues in mind instead. But at any rate, the game has artificially limited which characters you can use by making many of them unusable.
A form of Fake Difficulty, albeit one that may be hard for designers to avoid. Compare with Trial-and-Error Gameplay and Plot Tailored to the Party. Some fans try to overcome this with Character Tiers. See also Required Party Member, when you must have a certain character in your party for plot-related purposes (since you typically have a party of three, this may mean leaving a preferred character behind).
Pokémon Red and Blue: Of the three starter Pokémon, Charmander is the most popular, but makes the game more difficult in the beginning because he's super weak against the first two gyms' Pokemon. However, it's not particularly difficult to win with Char if you have any idea of what you're doing.
Other versions do this too, however they have been a little more merciful in the more recent years. Gold, Silver, and Crystal have this with Chikorita, who is at a disadvantage for two gyms unless you nab some types that are useful against flying and bug. (Fortunately, you can capture a Geodude relatively early in the game, which has type advantages over both if you can get it to learn Rock Throw.) Meanwhile Cyndaquil and Totodile are much better. (Although Typhlosion does start to phase out around the 5th gym, if one uses a single Pokémon the entire game, which is actually rather easy to do.)
While Typhlosion does start to phase out after a while, it's good until at least the 7th gym, since it has type advantages against the 6th and 7th leaders.
Chikorita is a negative version. There is only one gym where Chikorita has a type advantage, and it's ironic how a gym that uses a type advantage over it (Mahogany Gym uses Ice, but all of the leader's Pokemon are also either Water or Ground type, while Grass attacks do neutral damage to Ice). All other Gyms in Johto, Falkner, Bugsy, Morty (uses Ghost, but they're all part of the Gastly line, and thus also part Poison), Jasmine (to an extent since Steel-types are resistant to Grass-type attacks), and Clair (two of hers know strong Fire attacks) are all at an advantage.
Totodile definitely got the huge point in gen 2. It can grind in the Victory Road effectively(something that Typhlosion lacks and Meganium can), compatible with the infamous Disc One Nuke of said gen, has good typing matchups against almost every gym fights, has the tools to make the game's That One Boss easier, and its learnset supply it with the exact moves to beat the Indigo Plateau. The only cons from using Totodile are the fact that it evolve the latest, but the earliest to its third stage, and you can get both Suicune(in the Updated Re-release) and Gyarados through the story, although arguably neither has the movepool effectivity that Totodile carries.
Though this is all part of a deliberate structuring of the games, so that some starters are stronger later on, like Charizard (Charmander's evolution), some stop being useful after a while, like Venusaur (Bulbasaur's evolution), and some, like Blastoise (Squirtle's evolution), are average throughout.
In general, it seems like the water starter is the one that stays decent throughout, and the fire and grass starters are either good early and less useful later, or vice versa.
In Pokémon Ruby and Sapphire, the evil teams revolve around a specific type (in Ruby, fire; in Sapphire, water), so some people pick their starter based on that (Mudkip in Ruby; Treecko in Sapphire).
In Pokémon Diamond and Pearl, there are only two kinds of Fire Pokemon in Sinnoh. One of these is the starter Chimchar, which evolves into Fire/Fighting Pokemon that have some sort of type advantage in at least five of the eight Gyms (and Maylene's Lucario and Volkner's Ambipom). The other is Ponyta, which takes forever to evolve into Rapidash and even then isn't particularly great. Platinum thankfully fixed this by adding more Fire Pokemon to the region— Eevee (and by extension Flareon), Houndour, Magmar, and a possessed toaster ovennote Rotom. However, Chimchar is still one of the best choices for starter.
In Pokémon Black and White, the first Gym, at least, kicks the trope in the balls - the gym has three leaders, one of each starting element, and the one with the type advantage will always be your opponent. The leader in question will unambiguously point you to an easy side area where another trainer will donate you the third point in this Elemental Rock-Paper-Scissors to even things up.
And while choosing Tepig will make the second gym slightly easier, there is such a wide variety of types by the third gym that your starter choice is virtually irrelevant.
The sequels basically avert it-Cheren's normal-types in the first gym aren't weak to anything but fighting-type moves, so you either have to level up your starter and a couple other mons enough to take his out or go catch a Riolu at Flocessy Ranch and level it up so it learns some fighting moves. After that, though, Snivy will be at a disadvantage a couple of times (against the Poison-specialist Roxie, who has a mon with a double resistance to Grass-type moves; the Bug-specialist Burgh, who has two mons with double resistances; and the Flying-specialist Skyla, who has- you guessed it- a mon with a double resistance to Grass-type moves, although she has a mon who at least takes neutral damage from Grass-type attacks. Two of Drayden's mons resist Grass as well, but don't have any moves to counter Snivy).
Pokémon X and Y averts this for the most part. While the initial Gym being Bug-type may seem to be an easy advantage for Fennekin and a disadvantage for Chespin, the latter gets Rollout to compensate. In addition, the player is allowed to pick a Kanto starter in between the first and second badges, meaning that a savvy player would select the Kanto starter that could cover for the Kalos starter's weaknesses (e.g. Squirtle for Chespin). In addition, Wonder Trade being accessible as soon as the player catches a second Pokémon means that they can field a team that covers each other's weaknesses, provided they're patient with trading.
HM Moves can result in this, particularly in Gen III. Around 40-50% of Hoenn's traversable terrain is sea, so one will almost always require a Water-type and a Flying-type (for Surf and Fly respectively) purely for mobility. Fortunately, early routes gave you the Water/Flying Wingull.
This also shows up in the Pokémon Mystery Dungeon series. Normally, virtually every Pokemon is viable due to allowing you to use stat boosting items to compensate for any stat deficiencies (Unlike the main games). However, the dungeons that temporarily revert your Pokemon to a low level throw this out the window. The only Pokemon who have even a slight chance of surviving through one of said dungeons need to have high starting stats and/or high stat gains for their early level-ups and they also need to have a decent level-up moveset. Pokemon lacking the former qualities will get torn apart on earliest floors, while those who lack the latter will suffer for it later when the enemy Pokemon become too tough for their moves to deal with them efficiently. It becomes even more limiting if the dungeon also forbids bringing items and/or other party members, as they can compensate for the flaws of a given Pokemon to a degree. There typically ends up being only around a dozen or so Pokemon out of the hundreds available who can actually clear these dungeons with some semblance of reliability as a result.
Diddy Kong Racing (or at least, the N64 original) makes you try different characters constantly. In fact, the first Wizpig race is just about the only one where it doesn't make a difference what character you choose. Anything else either requires balanced middleweights or fast lightweights, except rare occasions where a heavyweight would keep you from being pushed into water.
Heavyweights and middleweights are ideal for Hovercraft races though, as the smaller racers bounce around way too easily.
Nintendo Power once had an article that rated the racers from Diddy Kong Racing; it was basically a scale from the lightest to heaviest racer, with Pipsy, the lightest, the highest ranked, and Krunch, the heaviest, the lowest. In fact, in their Guide for the game, for a particular turn they suggest just doing the race with a lightweight character if you can't make it.
The characters were finally balanced in Diddy Kong Racing DS.
There was an obscure Marvel Comics-based beat 'em up/platformer on the SNES called War of the Gems. The Hulk was so huge and slow that he was useless for nearly the entire game, but his range was such that he could interrupt most of the final boss' attacks, meaning that he manages to be an obnoxiously worthless character and a Game Breaker in the same game.
The Game Boy Advance version of TMNT 2: Battle Nexus. If you want to collect all the crystals, you have to switch between the turtles at least twice, as nearly all of them required a different one's skills to get to them
A Tiny Toon Adventures-based game on the NES allowed Buster to switch places with Plucky, Furball or Dizzy. The character to whom he switches is chosen before the level. Not only are many levels easiest with a specific character, but the game even tells you which character that is if you sit on the character select screen long enough.
In Wing Commander III, if you continue to choose to fly with Hobbes over the other pilots, past the first mission, you get called to the carpet on it by Captain Eisen, and morale suffers from the show of favoritism.
Most Kirby games require the use of specific abilities to access objectives or secret areas. However, since copying enemy abilities on the fly is Kirby's whole shtick, it's probably justified in this case.
One level in particular is made MUCH easier if you have Ayla in the group due to the fact you are imprisoned and all of your equipment is removed. If you get attacked by anything in this condition, you are screwed.... unless you have Ayla in the group. She is the only character who can use her bare fists to kill enemies. Just beware of the fact she doesn't have her armor on; she takes high damage until you recover your equipment.
When fighting Magus, Chrono and Frog are required, leaving you one slot open for either Lucca, Marle, or Robo. Except you pretty much have to bring Lucca, because Magus is the trope namer for Barrier Change Boss and Frog and Marle are both water magic users. So if you want to be able to break through three of the four types of barrier, she's out. And Robo is slow and has a pretty low magic stat, so while he has a dark-elemental attack, he's not a whole lot of help.
Guild Wars. There are numerous occasions, mostly in PvP, where if you are playing a particular class or build, you will lose. All the time. The developers have even admitted there are some builds and classes they specifically don't want players to play.
An occasional complaint about Mega Man X 8 is that obtaining all of the items more or less keeps Zero on the bench up until the fortress stages, leaving Axl (who is admittedly fun to use this time around) and X to do everything.
If you chose the Shadow Armor to complete Gate's fortress in X6, you WILL have to continue and change armor after the first stage because of a Bottomless Pit you can't cross. Everyone else can cross it, but Shadow Armor lacks an air dash. Ironic, since the Shadow Armor otherwise makes these final stages far easier with the immunity to spikes. You have to equip a specific combo of Parts (Hyper Dash and Speedster, but do NOT use Jumper or you'll go too high and hit a wall above you) before you start the stage and to have proper positioning to have a chance of making the jump.
Backyard Sports. The pros are usually the only viable characters to beat the game, except Lightning Bruiser Pablo. In fact, most of the rest of the Backyard Kids, who were only introduced two games before the pros, are awful in the games with the pros. Averted in Skateboarding, however.
Done particularily bluntly in Companions Of Xanth. Early in the game, you have to choose one of the four eponymous companions to accompany you on your quest: Jenny Elf, Nada Naga, Chester Centaur and D. Mentia. Three of these people will get you killed before you leave the first room. You're required by plot to choose only one specific companion. Worse, it is revealed later that one of the other three would have been a far better match for you, and you switch.
Similarly, Stationfall gives you a choice of three robot companions: your plucky robot buddy Floyd from the previous game, a tank-like utility robot, and a secretarybot. Choosing the utility robot results in instant death, and the secretarybot can't copilot the shuttle that is the only means of reaching 95% of the game.
The first had this in spades; the usefulness of your allies varied widely, with different ranges and 'wait times'. To make matters worse, certain dungeon floors would switch you to one of your allies without warning and force you to use them. Woe befall any player who couldn't adapt to the Mighty Glacier's awkward attacks after breezing through with the ranged characters...
In the second game, Red and Blue Seal floors would force you to use either Max or Monica exclusively, unless you used a special, consumable, expensive "unlock" item to let you use both like usual. The thing is, Max was generally overpowered because of his guns and his Ridepod Mini Mecha, so Blue Seal floors were just like any other to him; Monica was typically handicapped by Red Seal floors because these were almost always populated by Ridepod-class enemies against which swords and magic were almost useless.
The main source of difficulty in the Protector series of Flash Tower Defense games. Most stages require you to specialize in one or two specific elements, and sometimes specialize on one or two specific special abilities for your mages and combat specializations for your fighters.
Monster Hunter is typically nice about averting this, as a player with some skill can avoid timing out or getting pasted with any given weapon, but there are some fights that are much easier or much harder with some weapons. For example, Plesioth is typically a bow hunt because its questionable hitbox makes melee extremely frustrating. Fast monsters like Barioth or Blangonga are often easier with the sword and shield because it's easier to keep pace with them.
In the first battle against Drake in Advance Wars, if you selected Max or Sami as your commander and lose, Nell will outright ask you, "how about using Andy next time?". Drake's Super CO power damages all enemy units, while Andy's heals all allied units; it only makes sense. Of course, you need to complete the next few missions with only Sami in order to unlock a bonus boss...
Advance Wars Dual Strike has the War Room map, Megalopolis. This map gives the enemy loads of free income, negating the enemy CO's usual weakness of having better soldiers in exchange for having to pay more for them. However, there are six Com Towers on this map, which screams "Use the CO whose defense goes up when he captures a Com Tower or DIE!" There are also situations in Campaign mode where you NEED the CO who can lower the enemy power bar with her CO Power, but those are minor compared to Megalopolis.
You won't earn 100% Completion in Jumper Three unless you use every form of Ogmo. Yes, that means Blue Ogmo as well.
In Legend of Mana, going up against a certain dog-like boss on high difficulty with a glove class weapon was tantamount to suicide. Unfortunately, you won't know this until you're already in the fight and get hurt every time you punch him.
Final Fantasy III does this with job classes, as it was made in the days before switchable party members. Some dungeons force you into the "mini" status, which nukes the strength stat, so you have to switch everyone to a mage class if they're not in one. A few boss fights also require a certain job (eg Garuda and Dragoons) if you want to stand a chance of winning.
Final Fantasy X encourages the player to switch party members around regularly by making specific enemies suited to different members' attacks. Tidus deals well with fast wolf-type enemies, Wakka can aim for flying creatures, Lulu deals magic damage to attack-resistant flans, and so on. That's the carrot, the stick is the fact that if you don't switch they won't gain EXP for when you want them later It's really severe early on. Against the correct enemy type, each character normally gets a one or two hit kill. If you try to attack that same enemy with any other character, they will either miss or do virtually no damage. Only a handful of enemies you encounter aren't specifically made for one character to deal with. This mellows out later on when you can move into another character's part of the sphere grid to get similar stats and skills and can start customizing weapons. Kihmari tends to fall behind the other characters because there is no enemy type he is specifically made to counter.
Dissidia Duodecim will require the user to pick Cloud if he or she is going to farm money and weapons. Because the gateways are punishing to newer players (lvl 50-80 gateways when fresh characters are in their twenties), the player will have to bend the rules in the bonus scenario 00. Manipulating the rules to max out EX force, Wall Rush Damage, and Ex Damage is required to meet the goals in the gateways comfortably. Cloud's EX abilities suit the rule manipulation perfectly, so Cloud will have to be used in the majority of the fights solely because his Ultima Weapon can Guard Crush enemy blocks and can slam an enemy for almost all of their HP (save one since Wall Rush can't be the determining blow). As a result, the battles go quickly and comfortably. The scenario is certainly doable with the other characters, make no mistake, but Cloud's skillset and abilities are ideal to complete it for farming purposes.
It is virtually impossible to complete mission 18 of Ace Combat 5: The Unsung War, "Fortress", without an full-on attacker plane (i.e. a plane specialized exclusively in air-to-ground combat), so if you swept through the previous A2G missions in your fancy A2A fighter jet, you are in for a rude awakening. It is especially jarring since the very next mission is pretty much one big Hopeless Boss Fight against two squadrons of aces flying state-of-the-art air superiority fighters. And you are not allowed to change your plane.
Similarly, the last three levels of Ace Combat Zero: The Belkan War force you to keep the same plane and weapon for all three, regardless of what you actually go up against. Pick a dedicated bomber for "Avalon"'s trench run and you'll have trouble taking care of the enemy aces in "Demon of the Round Table"; conversely, go for a decent air-to-air fighter to take out those eight aces and you'll have to make multiple runs through the trench as it's slowly closing itself off.
Super Star Wars: Return of the Jedi employed this trope in spades. Some levels let you choose from a small pool of characters to use for a level while other levels forced you to use a specific character.
Example where the opposing team forces your hand: In Team Fortress 2, if you run into a wall of 2 or more sentries, you may be forced to switch from poor long-range classes like Pyro or Scout to specific Engineer-haters like Spy or Demoman.
Whether or not you lose team members during the Mass Effect 2's invasion of the Collector's base is determined solely by who you pick to fill what role. Pick the wrong person to escort the hostages back to the ship, or to crawl through the conduit, or to shield you from the bugs, and you'll lose people. Make the right choices, and you might get everyone through alive.
Alleviated by the fact that the selections make sense, and even the character description blurbs given on the screen do hint reasonably well at what choices should make more sense, such as Tali the tech genius for the conduit crawl and Garrus leading a commando team.
Not quite as bad as most examples because you should usually have at least two good options for each role (unless you, for some reason, decide not to get everyone loyal either through laziness or incompetency and decide not to buy any ship upgrades despite being told how useful they would be) and your options are normally similar types of characters, so it shouldn't be very common that your only options are solely your preferred party members.
The X-Men Legends games both have shades of this, because some enemies in various areas will be resistant to the kind of damage your heroes are dealing. The most egregious examples include the Morlocks, which will come in swarms of all the different kinds of resistance, forcing players to switch characters while in the center of a stampede; and the Sentinels and other robots, which are resistant to mental damage. Which makes sense in and of itself, but this trope really comes into play in the second game, where Jean is the only character who specializes in mental attacks and is thus useless against the robots.
Additionally, though he's not required, there is one part of the final dungeon in the world world where you come face to face with a door that's sealed shut on the outside and an additional switch inside its room must be thrown in order to proceed. Nightcrawler with his teleporting ability is the only way you can get through this part.
The Sky Babylon stage in Sonic Rush Adventure has a lot of fire scattered about randomly, which can get really annoying since you'll probably be moving too fast to avoid it in time. Blaze the Cat happens to be immune to fire, so unless you really want to do things the pointless and difficult way, you'll want to choose her.
Gloria Union has five main characters and (usually) only five deployment spaces per map, while your team will have between eight and thirteen members. All of those five main characters are repeatedly required-deploy late into the game, which forces you to use them to level them up instead of getting the chance to try out the rest of your party.
In Dragon Age II, unless Hawke is also a mage, Anders will be the only healer available for most of the game. Since only relying on healing potions is costly and risky (thanks to potions' cooldown time), Anders will probably be in the party most of the time. This makes the final decision concerning Anders' betrayal that much more difficult.
What makes this example particulary painful is that Anders lacks the Spirit Healer specialization and instead half of his unique skill tree, Vengance, consists of inferior versions of the Spirit Healer spells, while losing out on some of the helpful passives that exists there. Vengance's other half turns him into a glass cannon and is mutually exclusive. The two other mages, Bethany and Merrill? Bethany can only learn the basic heal spell and will be killed near the end of the prologue if Hawke is a mage, while Merrill can't learn any healing spells whatsoever.
Shadow Hearts Covenant and From The New World basically force you to take Anastasia and Johnny, respectively, because they're the only ones with the Enemy Scan move. It's not vital in Covenant, but you lose an entire gamewide subquest if you neglect to take Johnny anywhere in the latter game.
Very common in most MMORPGs, like World of Warcraft, where choosing the wrong group setup in endgame raiding can easily thwart all chances at success. World of Warcraft itself has gone from strictly this (The Four Horsemen were notorious for requiring eight well-geared warriors to beat) to a bring the player, not the class style of play. Instead of having unique abilities and buffs that may be required in certain fights, the classes are defined by different playstyles and any 10-player group is very likely to be able to beat any encounter, especially now that changing specialisations is much easier. Buffs in particular have been made comparatively weaker and more available.
League of Legends (and perhaps any other Multiplayer Online Battle Arena), being a game based heavily around teamwork, practically requires this. A properly balanced team of one tank, one fighter/off-tank, one jungler, one ranged DPS and one support will usually demolish a team of people who just picked their favorite champions.
The levels in Megaman And Bass were clearly designed with the Double Jump and the ability to shoot in 8 directions in mind, and only Bass can perform either (as well as fly). This is completely flip-flopped during the boss fights which were clearly designed with Megaman in mind, while Bass's machine gun can only inflict one sliver of damage every four seconds. And no, you can't change characters mid-game.