Here is list a revised form a while ago and submitted in another site. It hasn't been featured or anything, but I was wondering about what you guys thought of it.
(I know I left at least one notable character, but I didn't really played his game that much)

Also, what do you think about the topic itself? Personally, I has always bothered me the fact that almost every RPG hero HAS to wield a sword, and probably most of the party (unless they are mages. Then it tends to be the traditional staff)
One of the things I like about Shadow hearts is that they pretty much breaks this tradition. (A reason I didn't add Yuri to the list tho, is because the list is actually bladeless heroes, and he uses claws along with the knuckles)

Oh, this was only RPGs. I figured you would mean out of all games. If so, Samus, Solid Snake, and Sonic would be on the list. It's a good one, and it's nice to see Suikoden on there 3 times.

ooops, indeed. It was supposed to be RPG heroes (I just fixed the title) Swords are more common in RPG, and that's why I wanted to focus on swordless characters from that genre.
And I didn't want to put Suikoden 3 times, for the sake of variety, but each of them brings different weapons for a main character.

Rudy, Shion, and Ness definitely belonged on that list.

Rudy was the first of many Wild Arms protagonists to show us that guns are always better to bring to a fight, and Shion was proof that, in a futuristic age, you could be a total noob when it comes to fighting and still survive the battlefield time and again so long as you had a multi-trillion dollar global (or in Xenosaga's case, perhaps universal would be a more fitting term) corporation providing your weapon of choice. And that M.W.S. was no sword.

It was hard to fathom that Ness was the big-damage member of the party in Earthbound yet his weapon was a mere baseball bat. But sure enough, I guess that's why he was on the list.

I was about to add Yuri until I saw your reason.

Are we talking like, ANY RPG character, or just the MAIN protagonist. If the latter, then this just got a little more difficult.

I probably will settle on Ness, but I want to pick something that hasn't been mentioned already. So I think I'll go with Will from Illusion of Gaia. Dude fought with a flute.

Yes, I meant RPG protagonists, not just any character.
I never played Illuison of Gaia He would have been on that list if I did.

Keyblades don't count because they're swords smeared with some plot makeup.

Suikoden protagonists get a well-deserved mention.

The winner for me, though, has to be Croix from Ar Tonelico 2. The guy has a thing attached to his arm that works as a lance and it shoots missiles out of the tip. It looks like something a Gundam would carry.
Speaking of which, all weapons in AT2 are unusual and creative in some way. One support character puts two of her hair accessories in the ends of a quarterstaff and fights with that. Another character has two huge bladed yo-yos that he throws to shred things to pieces.

Final Fantasy V gets a honorable mention in my book because you can dance the jitterbug at enemies to damage them, and I have in my life not seen a better way to fight, ever.

About the topic itself – swords are in popular culture the "standard weapons", right? Fighting with a sword is showing a neutral personality. I think it goes together with the fact that most JRPG main characters (since we are in the end talking about JRPGs, western games are radically different in that aspect) are bland and devoid of any personality.
Giving someone any different weapon says something about the character himself.

EDIT: Gah, how could I forget? Demifiend, protagonist of Shin Megami Tensei: Nocturne, fought with punches and summoning demons to kill other demons. (The protagonists from SMT1 and 2, though, had swords)
The main from Persona 3 shot himself in the head to force himself to summon manifestations of God (or Satan or both) out of his own psyche. This gets second place to the jitterbug, in my list. =D

The main character from SMT: Devil Survivor uses a COMP (DS Shaped computer) to fight demons.