So far, I've been posting opinion pieces here. I think that having usable content as well is part of a good gaming blog, so I'm going to put up something I've come up with for Basic-edition games (B/X, BECMI/RC, Labyrinth Lord, etc.).
Attack rolls for very high level fighters can get to the point where they often miss only on a natural 1, and so bonuses to hit often become irrelevant. Also, against the high HP of very high level enemies, physical attacks can often feel weak compared to the blasting attacks of magic-users.
To try to solve both issues at once, I intend to "borrow" the concept of Power Attack from 3.x. I don't want to import the rule as-is, because I don't want Power Attack's 1:1 ratio for exchanging to-hit for damage. That's because it would, I think, be overpowered out of the 3.x context and become overly dominant, especially since 3.x characters need to invest a feat to have the option (no equivalent to that exists in Basic).
The basic Power Attack is available to any Fighter, Dwarf, Elf, or Halfling. This reduces the attack roll by -4, but if the attack hits, damage increases by 1d4. Greater Power Attacks are restricted to higher level characters (of the above classes only):
Level 2: -6 to hit, +1d6 damage
Level 4: -8 to hit, +1d8 damage
Level 6: -10 to hit, +1d10 damage
Level 8: -12 to hit, +1d12 damage