I play a bit of Play-by-Post and Play-by-Email, so I'm no stranger to its advantages and disadvantages. The chief of the latter is well known: it's godawfully slow. This makes detailed planning and complex inter-character interactions (the most fun aspects of RPGing, to me) very difficult if not impossible.
I've been thinking recently of using diceless systems as a way around this. Amber DRPG and (if I understand it correctly) Nobilis allow the player to take far more 'narrative control' than dice-lead games. In Amber, player-characters automatically succeed in any given task unless they are opposed by another player-character. In Nobilis, the spending of tokens achieves a similar effect.
This does away with one of the major stumbling blocks to progress in a PBP game, namely, the Everybody Waits for the DM Song and Dance Routine. This will be familiar to anybody who's tried a game with this format - whereas in a tabletop game the DM can give the players instant feedback on the success or failure of proposed actions, on the net the process becomes attenuated by log-in times, typing times and time zones, making creative thinking and problem solving a frustrating process at best. However, with a game like Amber, where success in many situations is guaranteed, this problem fades to insignificance unless two players are in conflict against one another - rather than the usual "Can I climb that wall/open that chest/break that vase" sort of questions that get posted in a trad PBP game, instead you get stuff like "I climb the wall, then at the top I open the chest and then break the vase". Hey presto, things are moving faster than the pace of a snail on barbiturates.
This only works for a specialised type of game, and part of the fun of traditional RPGs is that failure is a big possibility in most situations. But in the glacial world of PBP it may be a better option.
(There's a good thread on diceless games here at rpg.net. Occasionally that site does throw up something useful.)