As I work on the long-delayed playtest draft of Goblins & Greatswords, I've been pondering the combat system, specifically as it relates to fighter-type characters.
Fighters, as combat specialists, should naturally be more effective in combat. In most editions of D&D, this manifests primarily in terms of being able to use any weapon or armor, higher hit points, and better chances "to hit." Since combat is abstract, though, a single attack roll doesn't represent a single swing, but rather the sum of everything a combatant does in a round. It could mean one good solid blow among a lot of feinting and parrying, or it could mean a couple glancing slashes with your weapon, an opportunistic head-butt, and a kick to the knee. Fighters should be better able to perceive and capitalize on these opportunities, and so, in my opinion, should have the potential to do more damage per round.
Of course, better attack rolls do accomplish that, but the effect is overall rather trivial. A fighter who has an attack roll 4 points better than the cleric will do, on average, 20% more damage per round over the course of a fight.
AD&D gives the fighter a boost with multiple attacks, which are not only somewhat abstraction-breaking but also rather clunky in their execution. In order to avoid huge jumps in damage potential, there are "half steps" -- 3 attacks per 2 rounds and 5 attacks per 3 rounds, which means you have to remember whether you attacked once or twice last round.
Basic D&D of the BECMI line has multiple attacks at level 12 and above if the fighter can hit his target with a roll of 2, which is also quite wonky in my opinion, as well as having enormous stretches of little or no improvement followed by big sudden jumps. Also, I and many others would consider a campaign somewhat broken if PCs are regularly hitting foes 19 times in 20.
What I'm thinking of instead is to tie extra damage to the attack roll itself. At certain levels, a fighter gains the potential to roll an extra damage die for whatever weapon he's using if his attack roll is "x" higher than the minimum needed. Say, at character level 4, if the attack roll 4 or more higher than needed, an extra damage die is rolled. At level 8, a roll 8 or more higher than needed gets a third die, and at level 12, a roll 12 or more higher than needed gets a fourth die. These are only examples; you could tweak the levels and the thresholds for additional damage dice as desired. You could also grant other classes similar benefits at larger level jumps, e.g. maybe at 5th and 10th or 6th and 12th, or you could even give them at the same levels as fighters, relying on their poorer attack roll progression to make the benefits kick in less frequently.
In this scheme, armor never becomes obsolete as it tends to do at high levels in D&D. Even if a relatively low number is needed to hit at all, having better armor may keep the attack from surpassing the required roll for one or more extra damage dice, which is a fairly big deal.
Additionally, you could allow the player to apply the extra dice to other opponents within range, so long as the attack roll is good enough to hit them at the required threshold -- easy to judge if he's fighting a gang of monsters with the same AC, and only marginally more complex in a mixed group.
I'm thinking of applying this not only to characters, but also to monsters which traditionally have multiple attacks. Instead of an owlbear rolling three attacks for 1d8 damage, it rolls once, doing 1d8 on a basic hit, 2d8 on a roll 4 higher than needed, 3d8 on 8 higher, and in any case, the extra 2d8 "hug" on a natural 20. A giant who normally does 4d6 could have its damage broken down into d6 increments, easily wiping out several lesser opponents with a single good attack roll.
Obviously, more analysis and some play-testing are in order, but I'm cautiously optimistic about this method.