I just finished Pokemon Mystery Dungeon: Gates of Infinity in order to review it for the site, so I'll avoid saying much here except that I played as Axew who's dragon/dragon/dragon. :)

Um, Eternal Sonata sorta does....

NieR

Tales of Eternia you save TWO WORLDS. 
Plural'd the threat there.

Radiant Historia you temporarily save the shitty continent you're on.
...I don't think they actually "fixed" the problem beyond the "warring nations" A-plot though.

Breath of Fire III
You spare...your race?  And tell god to fuck herself so you can have nice things.

I"m going on a limb with Drakengard... but you spare your mind because how shit gradually turns to shit, and shitter, and shittiest.

My examples suck ass.

Baten Kaitos you save crops of continents that float in the sky and not a world.
..Hmm, Wiseman wanted to change everyone into a Magic deck.

Final Fantasy VII technically because

It usually is.

I actually used the magnifying thing with the light a lot...

Uuh, my bad. Yeah, then probably so. SMT III's boss battle was pretty repetitive, though the SMTI's battle theme has its charm.

Wait, are you working out every day? Because you'll see less returns if you do. If your only workout consists of strength training, then two days off a week are a must.

Soft, man.  Sooooftt...  (i'm kidding)

http://www.leenks.com/gallery2112.htm
Awesome year book "send off" pages

Couldn't tell ya.  Once I finish I'm done with Skyrim.  World is too boring for being so huge. 

UnReal World - Recently freeware; your only goal is survival.

Shadowrun (genesis/snes) - Pretty sure these were both essentially murder mysteries.

Ultima 4 - Your goal is attaining avatarhood, and while you help people out you're not saving the world.

New Vegas - The entire world isn't at stake and you can actively try to fuck it up if you want.

SaGa 1 - The world wasn't really in DANGER in this one, and arguably your party more went on a journey of self discovery. You help save some of the sub-worlds, but... that's not really the SAME. Actually I don't think the world's in danger in any of the saga games after RS3, for that matter.

Chrono Trigger - Your goal's to save the world in this, and you do create an offshoot timeline where Lavos never lands, but that's not in your original timeline and I think the actual theme was about the 'spirit of the planet' or whatever sharing its history before it died.

Terranigma - It's debatable whether you're saving the world or just fucking it up worse (and the save-the-world plot in its traditional sense comes in pretty late).

SMT: N - Trying to recreate an already-destroyed world in your own image.