I've been doing some tests in Arena Mode on weapons in the most recent version. The test methodology I use is a slightly modded arena with 100 2x1 walled cells, with a macro that allows me to copy a given warrior into each cell.
Here are some of the more general conclusions I have come to:
Fighter and Weapon skills give both increased offense and defense (parrying happens quite a bit if you are more skilled than your opponent). High Fighter skill is much better than being completely untrained, but is trumped by high Weapon skill (particularly given that Fighter trains at the same time as Weapon skills, and faster to boot).
High Dodging skill is a massive advantage in combat. If your Dodging skill is above your opponent's weapon skill, you are almost guarenteed to win the fight. Even if it is only the same or below your opponent's weapon skill level it still gives a noticeable edge. A recommended training regimen for adventurers is to find a monkey or similar creature, grab it to prevent it from running away, and then let it flail wildly at you while you practice dodging. Remember, if you can dodge a monkey, you can dodge a sword. Extremely high weapon skill levels seem to decrease the benefit of even equally high Dodging skill levels, but these are almost never encountered in practice.
Wrestling is near useless when used by the AI. Its most common maneuver is to grab random body parts or articles of clothing and then release them. Code that makes people with open hands favor using those to wrestle would likely help here, as then joint locks and gouging would be more common. As it is, the AI will gouge or execute joint locks if it manages to randomly use hands to grab a relevant body part, but is otherwise not very effective. It will also attempt to strangle if it grabs the throat (again at random).
In the hands of a player, however, wrestling is vastly powerful. It was shown above that an unarmed enemy dies horribly versus an armed opponent, and with a free hand, a player can wrestle an enemy's weapon away from them. Currently, the AI cannot pick weapons off the ground, so this renders the disarmed enemy near harmless. Even if this is ever corrected, a high enough wrestling skill would still likely allow you to play "keep-away" with the enemy's weapons.
A player can also go for strangulation, which is highly effective. A good chokehold takes down any enemy that breathes within a few combat rounds, rendering them entirely helpless and easily killable. If one has a high enough Ambusher level, it is possible to sneak up to someone without them spotting you, knock them unconscious, and swiftly dispatch them, all while remaining hidden. Of course, this method does not work on anything significantly larger than you are, or that does not need to breathe, which includes pretty much all night creatures and megabeasts.
Unarmed combat can work, but it is significantly less effective than an actual weapon. Most reports of success in Adventure Mode involve combinations of this with wrestling to render enemies unarmed or unconscious. Also, if your skill in unarmed combat becomes high enough, you will start to use it more and more even while wielding an actual weapon (due to either opportunity strikes or your unarmed combat skill being higher than your armed combat skill).
The tiers of materials for both weapons and armor is Adamantine > Steel > (Iron = Bronze) > Copper > Silver. Blunt weapons mostly ignore this tier, and are effective almost no matter what they are made out of so long as its density is significant. While increasing density makes blunt weapons slightly better, any weapons-grade metal other than adamatine is acceptable for them due to the narrow range of available densities.
Weapon attacks are divided into three categories: blunt attacks, "slashing" attacks, and "stabbing" attacks. Blunt attacks are obviously any weapons with the BLUNT descriptor. "Slashing" attacks are edged attacks with a contact area of 50 or greater; it should be noted that this includes the "stab" attack of all swords. "Stabbing" attacks are edged attacks with a contact area of less than 50 (and preferably a high penetration depth). In vanilla DF, the largest contact area below 50 is 20 (pikes and spears).
Blunt attacks seem to ignore armor of the level of iron or below, are somewhat blocked by steel armor, and quite often (but not invariably) blocked by adamantine armor. This seems to be mostly independent of the weapon material. Blunt weapons are somewhat worse than edged weapons against unarmored opponents due to the lack of bleeding. Always aim for the head to get crushed skulls and torn brains, as these are the only instant kills easily available with blunt weapons.
Slashing attacks are almost completely incapable of penetrating armor of the level of the weapon or above. Picks with their higher velocity multiplier seem to be the sole exception to this, and even then the damage mostly consists of bruises and the occasional broken bone, indicating that their normally edged nature is being converted to blunt damage by the armor. Quite realistic, really. However, if the slashing weapon's material is of a higher level than that of the armor, it will cut through the armor like butter.
Stabbing attacks can penetrate armor, with the degree of penetration going up as the contact area goes down. The level of armor that can be penetrated depends on both the material of the armor, the material of the weapon, and the contact area of the attack, but a good rule of thumb is that a stabbing attack can penetrate armor of at least one level above the material of the weapon. It may require a decent degree of weapon skill to do this, however, and extremities like the hands and feet seem most vulnerable. Note that morningstars are actually stabbing weapons with a contact area of 10, and large daggers have the uniquely small contact area of 5 on their stab attack. Large daggers can thus make effective anti-armor weapons. It should also be noted that the small contact area that allows stabbing attacks to penetrate armor makes them less likely to sever body parts, but since brain death kills everything with a brain, I find that this is not a problem.
A modded-in estoc (think a severely overgrown, weaponized icepick), created by removing the slash and flat slap attacks of a two-handed sword and reducing the contact area of the remaining stab attack to 5 instead of 50, went through armor of higher tiers (a silver estoc could penetrate copper, iron, or bronze armor, but not steel; an iron or bronze estoc could penetrate steel, but not adamantine; a steel estoc could not easily penetrate adamantine, but in the hands of a master swordsman and fighter it was quite possible).
Penetration depth does not have a huge effect on human-sized targets, but for large targets such as giants, dragons, or other various megabeasts it becomes essential if you wish to reach any interesting internal organs. The fact that increasing size also renders severs and decapitations significantly more difficult means that stabbing weapons such as spears have a noticeable advantage when fighting large targets such as megabeasts. Again, aim for the head to get brain shots. The only exception to this rule is bronze colossi and other large, sturdy randomized beasts without brains or other internal organs to target. For these, you will simply have to settle for cutting off their heads through many, many hits with a slashing weapon, lumberjack style. Make sure your axe is stronger than their body tissue!
Robes protect every part of the body except for the head, hands, and feet. Modded pseudo-adamantine "leather" robes protected perfectly against slashing weapons in arena mode (with the addition of adamantine helm, gauntlets, and boots to cover the remaining body parts), but testing is needed to see if true adamantine robes retain this property.
The current combat AI will always go for headshots while an enemy is unconscious. Thus, if the enemy is wielding a weapon which cannot penetrate your helmet and you are unconscious, you are completely safe. Note, of course, that blunt weapons will almost always penetrate eventually (even if they're just punching you).
Miscellaneous object users wielding two shields had an advantage over miscellaneous object users wielding only one shield.