My favorite adventure that I've run has to be The Sunless Citadel by Bruce Cordell. It was not only the first full-length adventure I played through, but it's also the first adventure I ever ran.
What I like about The Sunless Citadel is that it kind of breaks the mold for what I think of as a typical first-level adventure. Normally, for a first-level adventure, I think the cliché is “rescue someone or retrieve some item from some goblins or orcs, and get a few gold out of the deal.” Pretty simple stuff, really.
In contrast to that, The Sunless Citadel has a ton going on: the kobold/goblin feud, the goblins working for Belak, Belak and the Gulthias Tree, the mystery of the twig blights, and the missing adventuring party. Not only does it have all of that, but there's also foreshadowing and references to a dragon called Ashardalon, along with a map that leads to the next adventure in the series, The Forge of Fury. On top of that, there's even a dragon in The Sunless Citadel. What more could you ask for out of a first-level adventure?