Lets see..
Suikoden 1 and 2... Tir McDohl technically takes on a sort of "emo" persona in Suikoden 2 (if you import data), but it's all explained within the first minute you see him quite logically, and you should bloody well know already why if you were able to import data.
(MAJOR SPOILER ALERT: He's carrying around a powerful Rune that has this habit of killing people close to him, and he went into wandering isolation to prevent further tragedy).
Lets see, nope. No major emos there. The only other example I can think of does the unthinkable and matures in his brief side-quest (bonus points if you can guess who).
Breath of Fire - No emos here. There's dragons though. Well, something about dragons.
None of the Quintet games had any emos..they had rather metaphysical stories though, if you're into the pseudo-divinity thing. No room for emo when vague-"God" and vague-"Satan" are involved.
Ok. So lets go with post millennial jrpgs...of which I have played very few of.
FF10: Tidus was more of a whiny ***** than anything. A lot of people love his character, but I never really got into it. Whatever.
FF12: Vaan. More of a not-character. Really, I would have to give this one to Ashe, who has a logical reason to be conflicted even if she does have all the personality of wet timber.
Shadow Hearts...eh, I can see it. Never played it, but one of my close friends did.
Xenosaga: I really think this series had a more FUBAR and plot-contrivance-filled story than FF8. Everything after Episode 1 is just a mess. Ziggy is effectively a human machine and a Journeyman of the Ellipsis, but never really whines. He's more like a paperweight that kicks things with a robotic leg.
Never played any of the Persona or Shin Megami Tensei series (same thing?).
Tales of [x]/Namco Bandai.
Varies wildly. There is some argument to be made here for some of the games.
The games follow a very solidly predefined rubberstamp following the success of Symphonia in the US (at least for the US releases; I will not presume to speak for the Japan-only games).
There doesn't seem to be much of a basis for an argument here save for Squall.
FF8 and maybe some Tales character(s).
Way to go internet culture; take the exception and make it a stereotype.