Thinking seriously (again) about doing an Old School campaign, albeit one that has been heavily modified. One of the things I'm thinking of doing is eliminating the Strength bonus to weapon damage. [pause for effect] Well, not really. What I'm thinking of doing is integrating the strength bonus in with the weapon choices available to characters.
Essentially, the damage that a character causes in combat is based primarily on their class. Fighters do d10 damage, clerics do d8 damage, thieves do d6 damage, and magic users do d4 damage. If they wield a weapon in two hands, then they get a damage boost of one step, so a normal fighter wielding a greatsword will do d12 damage and a normal magic user using a staff will do d6.
The damage bonus from strength is applied to this value. Thus a magic user with a +2 damage bonus wielding a 1H would do d8 damage, and a cleric with a -1 damage bonus would also do 1d6 with a 1H weapon.
So not much of a change from normal, really. However the difference is that this damage is actually what determines the weapons that the character can wield. Thus the aforementioned magic user would be able to wield a longsword (d8) in one hand. The cleric on the other hand would only be able to wield a club (d6) damage.
This is because strength allows you to wield larger and heavier weapons more easily. If the weapon does not suit your strength and reach, you will be very ineffective in wielding it. Conversely a weapon that is inadequate to your strength and reach means that you won't be able to gain the full effect from using it.
Does this mean that fighters with a high strength bonus wield supermassive two-handed weapons in one hand? Well no. It just means that the weapon they do wield can be used better. This system innately assumes that fighters wield the best weapons in the game. Thus the ultimate 1H weapon for a human-sized character is in fact the Bastard Sword (d10). Increasing the damage bonus simply means that the character can wield it more effectively when battering you into submission.
Classes will also gain damage bonuses as they increase in level. I'm unsure at the moment whether these should be applied in the same manner as the strength damage bonus (affecting the weapons that may be wielded), or act as a permanent bonus (so a dagger wielder with this kind of damage bonus does d6 because they know where to attack). What I may do is allow either approach, so a character can learn to wield a larger weapon or use a smaller weapon more effectively.
For reference the damage caused by swords are Greatswords (d12), Bastard Swords (d10), Longswords or Broadswords (d8), Shortswords or Smallswords (d6), Daggers (d4) and Knives (d2). Other weapons follow a similar scale, although they may lose a step for a special ability (frex a Spear, which would normally do d8 damage, actually does d6 damage but can attack at reach [and more importantly keep an opponent at reach]). Similarly creature size (and thus weapon size) will alter weapon damage accordingly, so a shortsword (d6) for a Fire Giant (+3 Size) would be a Greatsword (d12) for a normal human (albeit a clumsy one because the furniture would all be wrong - but capable of being adapted by a skilled weaponsmith).