Okay, so I got to this train of thought as I considered mundane combat in "the real world," and I imagined that in most man-to-man scuffles people improvise their attacks and defenses on the fly and as the situation dictates. D&D doesn't handle that sort of realism very well and forces people to learn specific attacks or defenses and presume that they are always used and will always work. Then I thought, "well, what if martial initiators could use any number of maneuvers per encounter and used their maneuvers spontaneously?" And then I thought, "wait, what if for any given situation there were basic actions and lists of stunts, and everyone can always do the basic stuff and stunts are more class based and usable once per scene?" And thus we are now on the same page.
Now, I don't have a system written out for this, but what I'd hope to get out of one is a game in which a complete neophyte is given a situation and he tells his DM he wants to do something and the DM can say, "there's a stunt for that," and the newb is rewarded by not only having a mechanical representation of the cool thing he wanted to do, but by being mechanically relevant even though he's a newb. It also encourages the players to focus more on roleplay if they can be relatively assured that their actions will always be relevant. The game would explicitly encourage DMs and players to work out their own stunts for actions not covered by published stunts.
Stunts would be the game designers' attempts to mechanically cover as many imaginative uses of basic actions, or combinations thereof, as they possibly could. As such they would be applied universally across combat and non-combat situations. Player Characters would NOT learn stunts, but, ideally, the players controlling the characters would describe whatever actions they wanted to use in a turn and the DM would resolve them using stunts as they apply.
For example, PC 1 tells the DM he wants to leap from the overhang, swing from the chandelier while hanging by his feet, snatch the golden necklace from the Lady of the Court as he goes, and execute a rolling dismount into a sprint. The leaping part is certainly a basic action, but everything from there on should be resolved using published stunts.