I thought I'd try and catalogue a few different approaches, and see what other ENworlders have to say - both about the taxonomy, and about the approaches. I'll be giving examples from my own RPGing. I've tried to set up what seem like reasonably broad categories, based on distribution of authority around setting, situation and motivation.
A. Players kick off the action
Once we've agreed on our system and basic genre/context, the players build PCs and decide on the initial difficult/challenging situation their PCs are in. (In some writing about RPGs, that initial situation is called the "kicker", for obvious reasons.)
My examples:
4e D&D Dark Sun: One of the players built a Veiled Alliance agent from the Land Within the Wind - an eladrin bard/wizard. They wrote as their kicker "My Veiled Alliance contact is killed in front of me as we are about to meet". Another player built a half-giant (goliath) barbarian gladiator, who wrote as their kicker "I was about to cut his head of in the arena, to the adulation of the crowd, when the announcement came that the Sorcerer-King was dead, and they all looked away." So we started the session in the arena of Tyr, at the moment the death of the Sorcerer-King became known to the crowd. I moved the action between the PCs (these two, and the third), building on their kickers and also - because 4e D&D is a party-oriented game - so as to bring them together. The assassination of the contact was one manifestation of the revolutionary turmoil.
Cthulhu Dark: In one game, we agreed to a setting of late-Victorian London. One of the PCs was a "proper English butler" in the service of the 7th Earl of Norland. I asked the player why he would come to London, and he said that he was there to hand various documents over to the lawyers, given his master the Earl's mysterious absence. That mysterious absence was the springboard for the situation, and I interwove it with the other PC's circumstances - he was an American journalist reporting on imperialism for a left-wing newspaper. Because Cthulhu Dark doesn't depend on party play, the two PCs crossed paths a couple of times, and their storylines interconnected, but they didn't actually work together.
B. Players create PCs with motivations, GM does the initial framing
The difference from (A) is that the GM is the one who establishes the initial difficult/challenging situation, in response to the player-authored PC motivations and PC backstories.
My examples:
Classic Traveller: The players rolled up their PCs and we worked out what this implied - for instance, one was a young noble who had barely scraped a survival roll in his second term and so (in the version of the rules we were using) had to muster out injured after a half-term. On his one mustering-out roll he got a 6, and so started with an interstellar yacht. Two of his other noteworthy features we a high DEX and Gambling skill. So the player decided that he had won the yacht playing cards, but the losers suspected cheating and so had beaten him to within an inch of his life. It made sense, then, that he had met the PC with Medic skill while in hospital. I rolled an initial patron, an Imperial Marines lieutenant, and had her approach the PC working in the hospital - an Imperial Navy veteran whom (we agreed) she knew from his time in the service, to help her out now that her initial crew (the gambling NPCs) had lost their ship. Things unfolded from there.
Burning Wheel: One of the players created a sorcerer PC whose main relationship was with his brother, his former mentor but now possessed by a balrog. This character's main goal was to obtain items or magical ingredients that would help him free his brother. I started the action at a REH-Conan-esque bazaar, where a peddler of trinkets and curios claimed to have an angel feather for sale.
C. GM creates situation, players bring the evaluation and interpretation
I've never played Dogs in the Vineyard, but as I understand it, it is a classic example of (C): the GM designs a town ripe with sin and conflict, and the players, playing their Dogs, have to decide whether and how to "clean things up". At the heart of this approach is that the players, not the GM, decide what counts as a satisfactory resolution.
My examples:
Agon: Each session begins with the PCs - classical Greek heroes trying to return home after a great war - being washed up on an island wracked by strife in some or other form. The PCs (and the players) also receive "Signs of the Gods" as they arrive on the island - images or motifs or omens that suggest the nature of the strife and how they relate to the various Olympian gods. It's up to the players to interpret these signs, and as the session goes along to decide when and how to call on the gods for aid (within the limits of their resource, like Divine Favour points). At the end of the session, the players and the GM work out the extent to which the PCs pleased the gods and what angered them, based on the players' interpretations of what the gods wanted, given their signs and their aid. This is all tracked on a star-chart called "The Vault of Heaven", which has a constellation for each gods. In the last session I GMed the PCs pleased Artemis, as they had interpreted her sign as calling for the defeat of the monstrous serpent on the island, and had succeeded at this, and also Apollo, as they had revealed the truth about the serpent cult; but I also decided that they had angered Apollo, as they had allowed the leader of the healers on the island to be killed; and that they had angered Athena, who had not wanted the serpent and its cult to be defeated.
Rolemaster: I GMed a long - 10+ years - RM campaign that was a much more drawn-out version of (C). The PCs included samurai from a defeated family, an animal king banished to earth for wrongdoing in heaven, and various warrior monks. The PCs found themselves caught up initially in various earthly machinations that mirrored or reflected heavenly conflicts; and then took a stand in relation to the heavenly conflicts themselves. They ended up going against the wishes of heaven - whose rulers were bound by ancient laws and agreements - by dealing with an exiled god and redeeming a tainted god, in order to come up with their own solution to trapping an otherworldly threat who was returning to the world and threatening to destroy it.
D. GM creates situation, and players try to solve the puzzle
The classic version of (D) is a D&D dungeon like Keep on the Borderlands or Castle Amber: the GM creates the context and situation, and the players' job is to engage it via their PCs and sort it out - in the case of B2, they have to defeat the forces of Chaos and get their loot; in the case of X2 they have to escape the castle, again with plenty of loot!
My examples:
AD&D: I've run a few AD&D sessions over the past several years, using a mix of published and randomly-rolled-as-we-go-via-DMG-Appendix A scenarios. The most recent was a session of White Plume Mountain. The players rolled up their PCs, I read out a bit of the backstory, and then we commenced the dungeon exploration. In our session, the PCs initially got pretty hosed by the heat induction trap, but after a strategic retreat they animated some zombies to help them beat the ghouls.
Torchbearer: This system is inspired by classic D&D, especially Moldvay Basic, but uses a variant of Burning Wheel as its mechanical framework. Like Basic, the GM is expected to write up scenarios/dungeons. At the start of a new scenario, the GM is expected to set the scene - initially via outright narrative, but in later sessions this might come in-game via rumours or NPC patrons - and each player chooses a Goal for their PC oriented towards the scenario. Working towards, or accomplishing, one's Goal earns fate-point type rewards.
The Green Knight: This one is interesting, because the puzzle the players have to solve is not a "technical" or operational one like in classic D&D, but a puzzle of honour: each scene requires the players to make decisions about what to do in relation to the core elements (including NPCs) in the scene; and the GM has a list in advance that awards or deducts points of honour based on particular actions chosen by the players. It's that GM-list-in-advance that differentiates this from a (C)-type approach. Doing well requires a bit of luck, but also good knowledge (or intuition) on the part of the players about standard tropes for a fantasy Arthurian-type RPG. A further interesting twist is that in the final scene no list applies, and so the game suddenly switches from (D) to (C): when I ran it one of the players picked up on this and switched from an Honour-focused to Dishonour-focused strategy at that point, although his poor rolling brought him unstuck.
A. Players kick off the action
Once we've agreed on our system and basic genre/context, the players build PCs and decide on the initial difficult/challenging situation their PCs are in. (In some writing about RPGs, that initial situation is called the "kicker", for obvious reasons.)
My examples:
4e D&D Dark Sun: One of the players built a Veiled Alliance agent from the Land Within the Wind - an eladrin bard/wizard. They wrote as their kicker "My Veiled Alliance contact is killed in front of me as we are about to meet". Another player built a half-giant (goliath) barbarian gladiator, who wrote as their kicker "I was about to cut his head of in the arena, to the adulation of the crowd, when the announcement came that the Sorcerer-King was dead, and they all looked away." So we started the session in the arena of Tyr, at the moment the death of the Sorcerer-King became known to the crowd. I moved the action between the PCs (these two, and the third), building on their kickers and also - because 4e D&D is a party-oriented game - so as to bring them together. The assassination of the contact was one manifestation of the revolutionary turmoil.
Cthulhu Dark: In one game, we agreed to a setting of late-Victorian London. One of the PCs was a "proper English butler" in the service of the 7th Earl of Norland. I asked the player why he would come to London, and he said that he was there to hand various documents over to the lawyers, given his master the Earl's mysterious absence. That mysterious absence was the springboard for the situation, and I interwove it with the other PC's circumstances - he was an American journalist reporting on imperialism for a left-wing newspaper. Because Cthulhu Dark doesn't depend on party play, the two PCs crossed paths a couple of times, and their storylines interconnected, but they didn't actually work together.
B. Players create PCs with motivations, GM does the initial framing
The difference from (A) is that the GM is the one who establishes the initial difficult/challenging situation, in response to the player-authored PC motivations and PC backstories.
My examples:
Classic Traveller: The players rolled up their PCs and we worked out what this implied - for instance, one was a young noble who had barely scraped a survival roll in his second term and so (in the version of the rules we were using) had to muster out injured after a half-term. On his one mustering-out roll he got a 6, and so started with an interstellar yacht. Two of his other noteworthy features we a high DEX and Gambling skill. So the player decided that he had won the yacht playing cards, but the losers suspected cheating and so had beaten him to within an inch of his life. It made sense, then, that he had met the PC with Medic skill while in hospital. I rolled an initial patron, an Imperial Marines lieutenant, and had her approach the PC working in the hospital - an Imperial Navy veteran whom (we agreed) she knew from his time in the service, to help her out now that her initial crew (the gambling NPCs) had lost their ship. Things unfolded from there.
Burning Wheel: One of the players created a sorcerer PC whose main relationship was with his brother, his former mentor but now possessed by a balrog. This character's main goal was to obtain items or magical ingredients that would help him free his brother. I started the action at a REH-Conan-esque bazaar, where a peddler of trinkets and curios claimed to have an angel feather for sale.
C. GM creates situation, players bring the evaluation and interpretation
I've never played Dogs in the Vineyard, but as I understand it, it is a classic example of (C): the GM designs a town ripe with sin and conflict, and the players, playing their Dogs, have to decide whether and how to "clean things up". At the heart of this approach is that the players, not the GM, decide what counts as a satisfactory resolution.
My examples:
Agon: Each session begins with the PCs - classical Greek heroes trying to return home after a great war - being washed up on an island wracked by strife in some or other form. The PCs (and the players) also receive "Signs of the Gods" as they arrive on the island - images or motifs or omens that suggest the nature of the strife and how they relate to the various Olympian gods. It's up to the players to interpret these signs, and as the session goes along to decide when and how to call on the gods for aid (within the limits of their resource, like Divine Favour points). At the end of the session, the players and the GM work out the extent to which the PCs pleased the gods and what angered them, based on the players' interpretations of what the gods wanted, given their signs and their aid. This is all tracked on a star-chart called "The Vault of Heaven", which has a constellation for each gods. In the last session I GMed the PCs pleased Artemis, as they had interpreted her sign as calling for the defeat of the monstrous serpent on the island, and had succeeded at this, and also Apollo, as they had revealed the truth about the serpent cult; but I also decided that they had angered Apollo, as they had allowed the leader of the healers on the island to be killed; and that they had angered Athena, who had not wanted the serpent and its cult to be defeated.
Rolemaster: I GMed a long - 10+ years - RM campaign that was a much more drawn-out version of (C). The PCs included samurai from a defeated family, an animal king banished to earth for wrongdoing in heaven, and various warrior monks. The PCs found themselves caught up initially in various earthly machinations that mirrored or reflected heavenly conflicts; and then took a stand in relation to the heavenly conflicts themselves. They ended up going against the wishes of heaven - whose rulers were bound by ancient laws and agreements - by dealing with an exiled god and redeeming a tainted god, in order to come up with their own solution to trapping an otherworldly threat who was returning to the world and threatening to destroy it.
D. GM creates situation, and players try to solve the puzzle
The classic version of (D) is a D&D dungeon like Keep on the Borderlands or Castle Amber: the GM creates the context and situation, and the players' job is to engage it via their PCs and sort it out - in the case of B2, they have to defeat the forces of Chaos and get their loot; in the case of X2 they have to escape the castle, again with plenty of loot!
My examples:
AD&D: I've run a few AD&D sessions over the past several years, using a mix of published and randomly-rolled-as-we-go-via-DMG-Appendix A scenarios. The most recent was a session of White Plume Mountain. The players rolled up their PCs, I read out a bit of the backstory, and then we commenced the dungeon exploration. In our session, the PCs initially got pretty hosed by the heat induction trap, but after a strategic retreat they animated some zombies to help them beat the ghouls.
Torchbearer: This system is inspired by classic D&D, especially Moldvay Basic, but uses a variant of Burning Wheel as its mechanical framework. Like Basic, the GM is expected to write up scenarios/dungeons. At the start of a new scenario, the GM is expected to set the scene - initially via outright narrative, but in later sessions this might come in-game via rumours or NPC patrons - and each player chooses a Goal for their PC oriented towards the scenario. Working towards, or accomplishing, one's Goal earns fate-point type rewards.
The Green Knight: This one is interesting, because the puzzle the players have to solve is not a "technical" or operational one like in classic D&D, but a puzzle of honour: each scene requires the players to make decisions about what to do in relation to the core elements (including NPCs) in the scene; and the GM has a list in advance that awards or deducts points of honour based on particular actions chosen by the players. It's that GM-list-in-advance that differentiates this from a (C)-type approach. Doing well requires a bit of luck, but also good knowledge (or intuition) on the part of the players about standard tropes for a fantasy Arthurian-type RPG. A further interesting twist is that in the final scene no list applies, and so the game suddenly switches from (D) to (C): when I ran it one of the players picked up on this and switched from an Honour-focused to Dishonour-focused strategy at that point, although his poor rolling brought him unstuck.