This is another YMMV (Your Mileage May Vary) answer. It worked for a small group who enjoyed writing. It might not work for most groups, but I don't see a problem applying it to most games, including D&D. I've never played in a "real" play by mail campaign, but this is how we did it:
We had a great Shadowrun game going through my last couple of years in college. After graduation our careers dropped us all over the map. We managed to keep the campaign going, in a fashion, for a couple of years. Occasionally we'd get together in person, but most of it was done by mail (somewhere along the line it switched from snail mail to email, which tells you how long ago this took place).
The first thing we did was recognize that this was a way to keep the campaign and the characters alive. It was not a substitute for gaming, so in that sense it wasn't really Shadowrun any more. It was us advancing the Shadowrun story we'd started earlier, but without the rules.
The adventures wound up taking the form of short stories. There was a definite arc to each, and a well-defined beginning and end. I would start the ball rolling by writing an introduction that placed the player characters in danger. They were given a mission by a Mr. Johnson, or perhaps someone close to them was kidnapped, or the cops started coming down hard on the neighborhood Orks and Trolls. I'd also include several bullet points laying out potential directions in which the story might head.
With the setup established, the players would collaborate to come up with some ideas about how they would proceed, One of them would continue the story I'd started, writing in the details of how each member of the group would behave and what sorts of additional trouble they'd get themselves into. Then the next player would add more to the story.
I'd usually jump in after the second or third player-created narrative chunk and add some twists, flesh out the antagonists, and so on. I'd also add more bullet points to help guide the direction of the narrative. Usually after another couple of story chunks, I'd close the adventure with a final chunk. I'd then reward Karma Points primarily on the basis of how well each player advanced the story rather than on how many heroic feats of derring-do their character performed.
The rules were pretty straightforward:
- No PCs can be killed
- Players should feel free to place each other's characters in serious jeopardy, so they have to be cleverly written out of danger
- While the game rules are not used to determine outcomes, the parameters of the rules still apply (no made-up spells, your elf can't fire one Panther assault cannon from each arm)
- Only the GM can kill off a major antagonist
This approach worked because we all enjoyed writing. We also knew the personalities and motivations of the PCs well enough that we could construct stories that fleshed them out even further.
When we were able to get together for an actual game session we were all ready for action, and we didn't have that "taking the campaign out of mothballs" feeling. It was also fun because some of the stories we came up with between "real games" were among the best story arcs in the entire campaign.