First dungeon you explored as a player or ran as a DM.
The Caves of Chaos, naturally. B2 came in the box with my copy of the Moldvay rules, so that's what I ran for my players. We got some really good mileage out of them, too.
I know it's not a perfect module by any means, but it was a wonderful introductory module because it didn't conform to the way the rule book said things should be. Maybe some of this can be chalked up to its being written for a previous edition and adapted to B/X, but nevertheless it taught me a lot about how to break the rules - not in play, but in creating dungeons and adventures. First, there was the layout of the Caves, which conformed only in the vaguest terms to the concept of dungeon levels. More powerful monsters tended to be in the higher caves (reversing the conventional wisdom that deeper = more dangerous) but there were a couple exceptions even to that generality. Monsters were often modified slightly from the official rules. I remember the minotaur being able to hurl his spear and close for melee in the same round, for instance, and also wearing a coat of chain mail for a better AC than the book listing of the monster. The leaders of the various humanoid tribes varied a bit from the stats listed for leaders in the rule book monster descriptions, too.
Then there was that spell of direction confusion that confounded intruders into the minotaur's cave. I remember sifting through the rule books with the proverbial fine-toothed comb for the official write-up of that spell before concluding that it was something Gygax made up just for that particular place.
The Caves of Chaos also taught me a lot about making treasure interesting (well, non-magical treasure, anyway. Magic items were pretty ho-hum, but what else should I expect from an introductory module?) and hiding it. There were silver bowls and bottles of wine rather than the hoards of gems and jewelry that you'd get just by rolling on the rulebook treasure tables. I remember coins being sewn into the hem of a blanket used as a wall-hanging in one lair, a magical shield used as an herb tray in another, and a wand inside a gelatinous cube.
I made very little of one of the most celebrated aspects of the Caves, that of the factions of monsters that could be played against one another by clever players. We played it mostly as a straight-up dungeon crawl - not that there was anything at all wrong with that.