Fighters are the neglected children of Dungeons and Dragons.
Fighters have been chronically underpowered, compared to the other D&D fighting classes, such as the Ranger, Barbarian, Monk and Paladin.
I'm likely opening myself up for criticism here, but I feel very strongly that there should be some modicum of balance, if not between classes, then between the sub-classes within a class.
I'm not advocating some perfectly balanced, mathematical symmetry, as is trying to be achieved in 4e (though I am not critical of that attempt), but I don't think that a player electing to play a fighter should be disadvantaged in her "in-game performance", as compared to someone who selects a ranger or paladin, having the same ability scores.
In at least one of the iterations of D&D (it may have been AD&D and/or 2e) attempts were made to power-up the fighter class. Those power-ups included weapon specializations rules and extra attacks as you increased in level. You may be able to identify several other attempts.
The Swords & Wizardry Core Rules gives Fighters a special ability to power-up the fighters. When fighting monsters with less than one hit die, fighters get one attack per fighter-level, per round. So, if I am a 7th level figher, and I am confronted by a host of kobolds, I get 7 attacks against the host of kobolds, each round. Of course, if it is a host of gnolls, i'm limited to only one attack per round.
I like the idea of extra attacks for fighters, based on their level, as it is a simple mechanic, that simulates the additional combat proficiency gained as one levels-up. But why should the extra attacks be limited to situations involving monsters of less than one hit die?