All-too-often I see DMs who run OD&D, B/X D&D, or any other version of classic D&D fretting about needing to prep to DM tonight, but not having anything ready.
Also all-too-often these DMs lament the fact that they have a shelf full of 3.x modules that they don't have time to convert.
"Time?" I think. "What time?"
Seriously, folks--the beauty of old-school, classic D&D is that it's so damn flexible, fast, and loose. ANY adventure can be converted completely on the fly, if the DM has any passing knowledge of the system in which the original adventure was written.
I'll take it a step further, and demonstrate how to do it with a humanocentric swords-and-sorcery game, which even requires that you remove demihuman races and humanoid monsters such as orcs, goblins, etc.
I am running a game tonight--a Conan game using OD&D--and have decided to use one of Mongoose's modules for the game. This is so easy to do it's not even funny. In OD&D all you need to know is the hit dice of a monster to use it. The hit dice determine everything, from the creature's saves to its "to hit" score. Ignore every single element of any given creature or adversary's stat block except for its level/hit dice, armor, and weapons. Yes, this includes feats, prestige classes, skill ranks, so on, and so forth. At best, use lists of feats, skills, and prestige classes as guidelines for any special abilities the adversary might have, which you will of course improvise on the fly. Most monsters in OD&D get only one attack--there aren't many that have claw/claw/bite attacks. So that problem is solved right there.
If a monster is a common critter such as a ghoul, simply open up Monsters & Treasure and use the OD&D entry for it. Done.
For games that don't use the d20 system, there's almost ALWAYS some sort of statistic that demonstrates the monster's fighting capability. This can generally give one an estimate of the creature's level/hit dice. The classic TSR Conan RPG, for example, gives every critter a "Fighting" trait. This is the creature's Level/Hit Dice in OD&D. The same applies for the Unisystem. Average out the combat-related skills of the adversary (Hand Weapon, Brawling, Martial Arts, etc.) to get a level/hit dice. For Call of Cthulhu or Runequest (off the top of my head; I'm not an expert with these systems), divide any combat skill by 10, then divide the result by 3 to get the level/hit dice. Straight skill-based percentile systems are a bit tougher, though, as you'll need to make snap adjustments after you do so. For example, converting a CoC ghoul in this method gives it 3 hit dice rather than the standard OD&D 2. But by all means, accept that your numbers WILL need to be tweaked after you figure out the base. If you get a ghoul with your conversion that has 7 hit dice, chances are you need to seriously tweak, for example.
Rather than rolling hit dice (which takes time) I generally assign hit points based on a "just above average" to "near maximum" basis, depending on how tough I want the fight to be.
What about all those pesky DC-based skill checks? Toss 'em. You know what needs to happen. Just make it so. If you really want to simulate Gather Information (for example) with some sort of check rather than by pure role playing, default to an ability check, be it Wisdom, Intelligence, or Charisma depending on the character (whatever is highest should suffice). Don't worry too much about degrees of difficulty--that's not really in the spirit of OD&D. But again, if you absolutely must do this, divide the character's relevant ability by 5. The result (rounded down) is the bonus to a d20 roll when making the check. Reduce 3.x DCs by 5 since you don't have skills.
And never, ever forget the default rule of thumb in OD&D: most things happen, are noticed, or have a base probability of 1-2 on a d6. That rule is your best friend as an OD&D DM. Thieves have a base percent chance to climb sheer surfaces (they only fall 15% of the time); others can climb non-sheer surfaces (with hand holds or equipment) and only fall on a 1-2 on a d6. Personally if they fall I give a save vs. Breath Weapon for half damage when they land (they roll with the fall) but I tend to be pretty easy on my players.
So that covers the basics. Now, what about nonhuman creatures like Demihumans and humanoids? In a strictly humanocentric swords & sorcery game, just change them over to whatever the most accurate equivalent in your setting. Goblins, for example, easily just become degenerate pygmy races. Orcs are savage tribesmen. Ogres become cannibalistic man-apes. And so on and so forth. The beauty is, nothing else needs to be changed save for the flavor and description of these creatures.
In this manner, you can pick up and run any adventure you like with no prior extensive prep work aside from the usual reading of the module. Remember, in OD&D, never sweat the details. Make them up as you go, and your players will never know the difference. It's a game that's designed for such snap judgments and on the fly adjudications, and despite what a lot of people like to claim, that's definitely a feature rather than a bug. OD&D is probably one of the easiest and most DM-friendly games ever written. The possibilities are limitless if you're willing to open up your mind and make it up as you go.