DMMike, I have a lot of experience sparring with heavy weapons. In my limited experience with LARP and SCA, only very light weapons are used there, but in our own fights we used weapons of authentic weights of 2 pounds or more. When we were smart, we kept our weapons padded with cloth, although once I sparred outside at night with solid metal poles around 4 feet in length. (I deserved what I got that night!)
I can tell you from very small fights (2-3 fighters) that the crucial element of melee is creating an opening, seizing the "right-of-way," or, as Fechbuecher call it, gaining "time" on your opponent. Battles do not even remotely or for a single moment take the form of any conventional roleplaying game, with each combatant whacking at someone in turn, because almost any time you attack an opponent who is on guard, you open yourself up to be struck.
Instead, one person will maneuver into position to attack, and then take the chance. If he fails, he will often be struck in retaliation. Sometimes one person will maneuver so well, or tie up his enemy's weapon cleanly enough that he can strike and be almost assured of a hit. When one person is struck solidly by a heavy weapon, he is usually not in any position to strike back; I suspect that with real weapons that damage on impact, this effect is even greater. The exception to this is sudden strikes made without a strong set-up, which are usually aimed at the lower leg; then the result is often a trade of blows with the other person striking your head, but you can sometimes get away with the free hit.
The next most important element of real life melee develops from the above: the person you fight takes almost all of your attention. If you are engaged with two opponents, you must retreat, circle, and use the terrain to ensure that you won't open yourself up to being hit by one enemy when you attack the other. But a lone fighter may at least hold off two assailants if he concentrates on defense; since he doesn't open himself up frequently, it is difficult to land a hit on him (particularly if he is protected by a shield).
A third crucial point is that of range or reach. I may infer that daggers are excellent in the crush of very close range ("mugging range") and also when one wishes to strike by stealth or get past the armor of a downed enemy, but I have no direct experience with this. What I have seen firsthand is that the dagger is an ineffective weapon. This is not necessarily because it deals less damage, but definitely because sword- or axe-men can attack a daggerman with impunity. Daggers are also weak on the attack since strikes to the knee or below are difficult to make. Worse and perhaps more importantly, daggers are too short to parry effectively, or to snag and "feel out" an enemy weapon. A shield goes a long way towards ameliorating this weakness, since one can block and control an opponent's weapon with the shield. Still, range remains a major issue.
Lastly I want to mention the importance of shields. The shield is a great help, because one is less open after attacking (and indeed under all circumstances) with a shield. In my fights with shields, I found that distances tended to shorten, since spacing is a fighter's primary defense, and with less need for defense one wants to get closer to improve offense. Legs and head both became more attractive targets on an opponent with a shield than the center, because they are generally exposed by small or medium shields. (This may not hold with tower shields.)
I'll conclude by noting that if most rpg designers had wide experiences with classical martial arts, fencing, and dueling with heavier weapons, most popular mechanics dominating the landscape of today would be regarded very differently. The classic turn-taking system would still have its place, but no one would attempt to argue in its favor on grounds of verisimilitude.
