I'm guessing that not too many people use 0 level adventures. Up until now I'd be one of them. There are a few published modules that use 0 level, but I don't think I've seen anything that I found to be that interesting. I started thinking about the idea after seeing the DCC RPG beta rules. After giving it some thought I've decided I am going to start my next campaign with 0 level characters. Here are some reasons why.
The chance to explore the transition from "normal" person to adventurer. What makes an individual an adventurer? What events set them on that path? Where did they learn their trade? I want to explore these questions with my group. I also really like the idea of establishing who the character was before they were an adventurer. The DCC RPG uses a table that reminds me of WFRP, where one rolls % dice to see what sort of mundane existence they had before they started wandering around in dungeons. Farmer? Rat Catcher? Mule Skinner? Tanner? All of these are possibilities, and they serve to define what sorts of skills and starting equipment the character has, as well as their place in the world.
I want to have a game with a "tight" economy. Starting characters aren't going to have much in the way of money or belongings. I want the first adventure to explain why these characters have the equipment that they have, because a sword and armor of any sort are extremely expensive. Treasure should actually mean something to the players, and being able to go back to town and get a proper suit of armor and with their first haul should be something to shoot for.
The last reason for me wanting to run a 0 level adventure is a little selfish. I had decided a while ago that if I was going to start a new game, I was going to use "classic" published adventure modules. Still, I'd like to run something of my own creation at some point. Since there aren't any published 0 level adventures that I would consider classics, this gives me the perfect opportunity to interject something that I have designed personally. This also gives me the chance to put to use the wealth of information I have gathered from all the blogs and other resources I have been reading recently. There is a lot more information around today to help GMs build a good adventure than there was 20 years ago, and I plan to put that to good use.