There are many RPGs in which you create a party of adventurers, and you can typically choose a class for each one (though some use classless skill systems, like Wasteland and Dragon Wars). While this provides a lot of freedom, there are some RPGs where a specific class or skill is needed to progress the game. For example:

Might and Magic 4 requires that you have access to the Teleport spell. If you do not have a Sorcerer or Archer, the game is unwinnable unless you manage to get a random item that casts that spell when used. (Why can't Rangers or Druids use that spell? It really feels like they should.)

Wizardry Gaiden 3 has locked doors that you need to pick to progress. The only classes that can do that are the Thief and possibly Ninja, and having a Ninja in your party is not going to happen at this point (you need 40+ bonus points at character creation, and I'm not sure if that's even possible; the max bonus possible in Wizardry 1 on the Apple 2 is only 29). Bards and Rangers can replace Thieves as far as chests are concerned, but they are completely inept at picking locks, making it impossible (or nearly so) to continue without leveling one up. (This is perhaps the worst example of this I have encountered.)

Elminage Gothic has a more tame variant of the previous requirement; more classes can pick locks, and none of the areas behind locked doors need to be explored until it's time to access the final post-game dungeon, at which point leveling up new characters to decent levels is quick and easy.

The Bard's Tale series has similar requirements. The first game has one spot where you have to use a Bard to reveal a door or a spellcaster to bypass the puzzle with a spell. The second game can't be beaten without an Archmage. The third game has the most requirements; you need a Chronomancer to access anything past the starter dungeons, one area requires spells that a Chronomancer can't use (so you need an Archmage), and the final dungeon requires using an item that only a Rogue can use, as well as one only usable by Warriors, Paladins, and Geomancers; that's 4 requirements (though you have some flexibility over the last one).

Do you think this is good game design, or should games be designed to be (at least theoretically) beatable with any party? Or does it depend? (I think WG3's requirement is not fair, but I don't have a problem with EG's requirement, for example.)

I kind of hate when a game forces you into bringing a certain type of character (particularly if they have given you the option of building your whole party).

I find Rogue's to be the worst case of this as they are often a really rubbish class but the only way to access a host of chests and secret locked areas.

I can't think of any specific games I've played where this was the case though..

Actually, one of the games I mentioned, Bard's Tale 3: Thief of Fate, did something interesting with the Rogue class. In that game, Rogues (especially at higher enemies) can instantly kill any enemy in the game just by hiding in the shadows and ambushing the enemy; furthermore, there are at least 2 bosses (one being the final boss) which are clearly designed to be won this way. The boss keeps summoning enemies so you can't advance into melee, while a Rogue can keep hiding and ambush the enemy. In other words, you would *want* a Rogue in your party even if it weren't required.

I don't think its good design to force players to have to play specific classes in order to finish the game, the example you gave with bard tales makes it feel like you have to roll a very specific party to win the game and there's barely any room for experimenting and replayability. However, I expect that everyone with some experience in RPGs knows that its usualy better to roll with the classic fighter/wizard/healer/lockpicker quatuor in your party as an implicit rule.

I'd say that a player should be able to finish a game regardless of the classes chosen for the party. By finishing I mean merely fulfilling the main story (and not necessarily in all possible ways). A player should not expect to loot all chests, to fulfil all side quests, to kill all enemies, to visit all areas, to open all doors with any class combination. Sometimes a game may provide additional means to bypass class restriction (usually scrolls, potions or magical items), but it is not a must. It is also OK for a game to have different possible endings for different classes (for example, only a bard can play a song and charm the final boss or his second-in-command).

I don't usually like replaying a game so I expect to unlock all content whatever party I choose. The game can always provide different ways to solve a quest. Locked door / no thief / no mage with "knock" spell? Fine, go fight that beholder and get the key.

Depends, the examples you mentioned seem too specific to me and hardly predictable for a new player who doesn't know what to expect...that's bad design imo.
On the other hand, it makes a certain amount of sense that you won't be able to open many locked chests etc. when you don't have a character dedicated to lockpicking. Even then there should be some workaround however (had that problem on my first playthrough of Baldur's Gate 2...only had Nalia as a thief whose thief skills are rubbish and can't be advanced anymore...had to rely on knock a lot, and traps were a problem...).

Do cases of Linear Warriors & Quadratic Wizards count?

On a better case, there's actually a dungeon in Final Fantasy 5 that while optional, does play with this idea in that half of the tower must be conquered by warriors, and the other must be conquered by mages; but the duality is opposed. If you use physical attacks on the magic user, they use a spell that restarts the battle. If you use magic on the physical fighter, they smash your face in

Final Fantasy 5, however, has one mechanic that makes it a non-issue; you can instantly change the class of any character, at any time you can access the menu, and the character's stats and abilities will instantly change accordingly. Also, at the point you can access this dungeon, every buyable spell is available in a shop that can be reached at that point, so if you didn't buy any spells up until this point, you can do so.

Also, your details aren't quite accurate. On the magic side, only the boss can restart the battle (and it's possible to prevent that by silencing it (what, the boss is *not* immune!?)); other enemies counter differently (for example, by using two attacks that deal 9999 damage (unblockable) each). On the physical side, during the boss fight, your magic is disabled, so you can't even try to use magic. The boss doesn't have that restriction to my knowledge (and will try to cast a spell when it dies), but it start the battle with no MP (so the spell will fail unless you use an Ether on it).

The PSX version's translation does have a major issue here; the person who is supposed to tell you which side is which lists the same side for both, making that information useless.