[Edit: I've edited the title to change it from "most famous?" to "famous?", as what I was hoping to do was separate the very noteworthy quests from the more run of the mill ones. I imagine we can all agree that clearing the Nashkel mines and saving the Grand Dukes (at the same time exposing Rieltar's original plot) are pretty much the most noteworthy.
To clarify, I'm not talking about considerations relating to game balance or the rules. I'm asking what actions would become widely known and talked about approvingly by the inhabitants of the Sword Coast, both common folk and in positions of power.
Off the top of my head, I can think of:
(1) Clearing the Nashkel mines;
(2) Finding the bandit camp AND killing the mercenary leaders (provided the Flaming Fist know about it*);
(3) Freeing the slaves in Cloakwood (provided they make it out of the forest alive*);
(4) Killing the Ogre Mage in the sewers of BG city;
(5) Killing Bassilus for the governor of Beregost;
(6) Clearing Durlag's Tower AND rescuing Dalton;
(7) Maaaaaaybe clearing the Firewine Ruins for the folk of Gullykin;
(8) Maaaaaaybe killing the wyverns for the governor of Beregost.
That's about it. The asterisk next to (2) and (3) is in recognition of the fact that this doesn't happen in the game and/or doesn't really seem to be given much consideration.
Notably, Scar's Seven Suns quest gives +2 rep and is not on that list, while his Ogre Mage quest is on the list and gives no rep in-game. I can totally see the Seven Suns quest mattering a lot to Scar and the Grand Dukes, but I don't see it mattering to the wider world in the same way the Sewer Ogre does (as well as mattering to Scar et al).
Anyone have an opinion on the above?