I would argue from practice and actual mechanics that properly trained unarmed melee fighter is just as dangerous as armed one - the only difference is that it requires a lot LESS effort to train someone to the so-so level with a weapon. This will serve as a motivation for the answer to Your question which will be at the end of the text.
I have 5 years of experience with karate kyokushin, 1 year of aikido and rather considerable experience with biology if someone is curious. I assume zero magic setting. I dare You to change this assumption :P I double dare You in fact ; )))
1. Ever wonder why boxers fight with gloves? Without them, fights would be very short. Put aside illusions from '70 kung fu(ry) movies and Matrix/Dragon Ball dances. A single strike to the nose/jaw/temple made by an experienced (say, 10 years of training 2-3 times a week) fighter shuts the target down, period. The target just collapses like a doll. I've seen it, I've experienced it first hand, there is no magic, brain is fragile.
2. We, westerners, are physically very weak, but properly fed (so, not peasants) people in any kind of more low level tech setting have enough strength to break a rib or two with a single strike. Again, this requires a solid bit of practice - I would say 3 - 5 years of training depending on a person.
3. Joints, joints, joints. Strikes are good and nice, but sometimes You don't want to be nice, You want to be effective. Roots from which aikido came from is where You want to go. Just as any japanesee-originating modern martial art, aikido has it's (arguably forgotten and very deep) roots in sengoku era battlefields. These people didn't have time to play around, and thus with some digging you can discover an array of split second grab, twist and horribly break manouvers, be it against unarmed opponent, long sword, short sword, knife, polearms, whatever You need. The kind of manouvers which leave victims shrieking in pain and completely destroy joints. 523
In modern aikido you can find reminiscences of this forms, very very malformed and 'civilized', but once You discover where they come from and read how they worked, You can imagine the originals pretty well. The caveat is, and I cannot stress this enough, they require A LOT of practice to pull off - tough once mastered, they are not as hard as they seem to be, its mainly a matter of reflex and precision. I think ikeda aikido is Your best friend in terms of youtube movies inspiration.
4. Throws for teamwork. Want to be nice support? Throw the target at Your friendly neighbourhood damage dealer. Catch his strike, redirect his momentum, bash his forehead with Your elbow for bonus stun/confusion and launch him at the pointy iron of Your colleagues. Again, watch some ikeda aikido, but mostly read about it's sengoku and bakufu roots.
5. Mobility and nasty strikes for support. Tracking two opponents at the same time is very, very, very hard (a thing which most rpg mechanics ommit unfortunately - poke Your gamemaster until he houserules this!). So be everywhere, distract, move, annoy, that ALONE makes it more difficult for Your opponents. Want to do more? Sure. Eye-strikes with extended fingers are very difficult and thus very situational, but kicks to the leg joints are super-fast, easy and very dangerous, because in melee combat a proper footing is EVERYTHING. Bah, even a properly timed low-kick can destabilize the opponent enough to be unable to block the next swing from that STR 18+ barbarian - and that's the end for the opponent probably. People typically dont bother with groin armour - well too bad because You have practiced your legs to hell and again, and really, a single strike to the groin is all the opening Your team sword wielder really needs and then some. Jump around, get to their sides, knee strike to the liver/kidney and watch them SUFFER, because this points hurt A LOT and it takes enormous willpower to even try to dodge after getting hit there - and mind you, most medieval armors, especially heavier ones, were often unprotected from the back because they were simply too heavy already. <PERSON> forbid they allowed You to get to the base of their neck. When situation is not giving You opportunities, strike at their muscles to sap their strenght, strike at their weapons to create openings for Your teammates, throw stuff because why the hell not - distraction is an extremely potent weapon (again, underestimated in typical rpg mechanics, but thats up to You and GM). 358