VI for pretty much the reasons chionos outlined. Several others have strong claims to being depressing as well (let's not forget that the world of FFVII is controlled by an evil corporation that drops a plate on Sector 7 just for funsies because of "terrorists") but I think VI beats them all because almost all of the central characters' stories are inextricably linked with the intrinsic tragedy of the game to an extent that simply isn't found in other games of the series.

That said, I'm told Tactics is mighty depressing as well, but I haven't played enough of it to evaluate it. (I suck at SRPGs).