Is it inevitable that an 'end game' will emerge or is it a conscious decision by the developers?
To start it is necessary to have a definition of end game. In mmos this is easily seen as the content after the level cap. At this point the manner of progression changes. I will use that: dramatic and 'permanent' change in progression. Permanent is not permanently permanent due to expansions adding to level caps, but the idea stands that within this version of the game the manner of progression changes and does not revert unless you move on to a new version.
Most games have some type of builfup of challenge and complexity. In a fps this can mean more weapons to use, new stronger enemies, and possibly tighter ammo or time limits. Together these will push a player to develop better tactics, faster reactions, and better aim*. However, merely pushing a player to play better does not create an end game. The progression model of "shoot enemy, use environmental trigger, move to somewhere is retained. Even dramatic shifts such as vehicle combat or even 'spy' levels do not create an end game since most of the progression is the same even if visually different and these are usually only single missions rather than full campaign arcs. More subjectively, when Vehicle fights do end up as final missions I tend to hate them for ending the game with the wrong feel.
On the subject of RPGs, pardon my limited scope, as I've only played a handful, the majority of which were Knights of the Old Republic (and Torchlight, which you should definitely try). But again, there's not a strong concept of end game. While leveling happens and there is a theoretical cap, that cap is based on possible enemies, quests, and specialization choices. There isn't a time when kills stop advancing your character (I'm assuming you're not looping back to low level dungeons). RPGs and FPSs do have boss battles, but these are mostly isolated incidents rather than entirely new phase of the game.
Past RPGs there are the MMORPGs, which historically are related to RPGs but at times may seem to have little relation. These have strong end-game concepts. There are level caps and past them the game changes dramatically. Experience ceases, often replaced by reputation grinds. The scale of content changes with the rise of raiding. Expansions may raise the level cap, but again, the cap is reached and a new end game is set.
I've been playing Civilization IV due to lack of computer power for the latest fifth. In it I notice that an end-game also emerges, though it can be very quick (as far as civ games go). Early power is gained by expansion. Barbarians are the greatest threat and land is waiting to be settled and turned to use. Workers and settlers are the drivers of growth, building new cities and improving the landscape. Military power matters, but it is not what grows the civilization. Until one day a settler wanders out and hits a strange colored land: the territory of another civilization. It is now that the settlers are workers are done. The land is civilized and improved. Now to get any further it must be taken. Peaceful expansion ceases to be possible. This is the end-game. It can be a very long one and seems to defy the label of end, but the same concept is there of a dramatic and permanent change in how one progresses.
I can see how a game like civilization could have no, or only, end-game. Scenarios could create fully grown and developed civilizations to battle it out. But is this truly different or just auto-play of the expansion phase, comparable to how a new WoW character is created with stats in place rather than players needing to assign them manually; it doesn't alter the fact that a new character is created.
Perhaps it's only a genre thing. MMOs will have an end-game and RPGs will not. FPS will not have one, but instead will have boss fights. But maybe I'm missing a critical factor: how we pay for games. MMOs have end-games to keep us playing and paying our subscriptions, while a single-player game would front-load content to get us to buy the initial box. But that's changing with the rise of downloadable content which isn't quite an expansion but still adds to the game.
Maybe I'm looking at it entirely backward and there is no end-game at all, instead some games have pre-game content that merely delays the coming of end-game, either to gain subscription time, to introduce a story, or to teach the player.