This is a question I have been asking myself. And to preface, I should say that I am speaking mostly about RPG's/Sandbox games. As long as story telling has been an art form, storytelling of all media has generally followed a predicable arc. But in an RPG, is this really necessary? Take Fallout3 for instance... Outstanding game IMO, but I found the Primary story line to be quite bland as the game drew on. The side quests however, and even just exploring and playing through what I call the "unlisted quests" were much more interesting to me. Could an RPG work as simply a collection of side quests with no central vein? Can characters and game worlds be constructed and driven based on nothing more than the philosophical, moral and ethical implications of the player's actions during chance encounters?

Many of Will Wright's creations qualify as sandbox games without a story arc. Things like the Grand Theft Auto series could work well without a story element too, in my opinion. Some of the items mentioned at http://en.wikipedia.org/wiki/Non-game may or may not also match your description.

As for RPGs specifially, it really depends on what your definition of the genre is. If all you care about is the mechanical system, there's no reason for there to be an over-reaching story arc or even any story at all - plenty of hack'n'slash RPGs fall into this category, for example, as do many MMOs.

God games and roguelikes are good examples...I have never played an MMO,so I could not speak to that. I think putting the player in a real, breathing world (like a GTA universe) and just surround them with with innumerable miniquests (the outcome of which would naturally alter the character's development) could make for an intriguing gaming experience. Conceivably, the traditional RPG system could be replaced with an immersive "episodic" experience...

Does this type of thing sound interesting to anyone?