I think that the best type of house rule for oD&D is the one that adds detail to the game without introducing new mechanics. That's why I'm going to begin to resolve my fantasy combats with the "Alternate Combat Sequence Method Number 3" found in the Swords & Wizardry Complete Rulebook on p.37.
This alternate combat sequence emulates (and streamlines) the combat resolution system introduced in Eldritch Wizardry. The streamlined combat system divided a round into segments of time. Participants act on a segment that is determined by various factors. The combination of these factors also determine when a character's subsequent actions will take place.
The Alternate Combat Sequence addresses some of the issues raised by many people who dislike oD&D: randomness and lack of detail. It elaborates on information that is already available to anybody that creates a Player Character in any version of oD&D. It takes into account decisions made by the players (such as armor worn and action taken) and reflects them in a tangible way within a combat sequence. It is a relatively simple way to add some details to oD&D combat that feats, skills, and maneuvers add to newer versions of the game.
At the end of the day, this alternate combat sequence will not satisfy gamers that like a lot of tactical detail in their game or those who like to keep things ultra-LITE. I think it's a good halfway point for both camps to meet for an exciting session of D&D.