I, like almost every other gamer on the planet has had times when it was damn near impossible to get a group together to play a game. In the old days that generally meant spending your time rolling up a billion characters, drawing a thousand dungeons and designing a couple of campaign worlds. However, with the invention of the internet, gaming was able to enter a new frontier. Admitted, there are some signs that say this new frontier might be slowly destroying pencil and paper gaming, but on the other hand, it has also given gamers the ability to contact one another a lot easier.
In the early days of the internet, a system called play by email was adopted by gamers seeking games online. This was a great option for people who either couldn't get a group together or had real life constraints (work) on their time. You simply checked your email, read a post or two, replied, and off you were. It was a short and simple way to get a small fix. In fact there were some PBEM's that I was involved with that were just as good if not better than my average tabletop session.
Along with PBEM gaming, play by Post gaming also started. While Play by Post was a similar way to game it was conducted on message boards. You generally had to create a username and then apply to a variety of games. While I strongly preferred PBEM gaming at first, there was a utility available in PBP that eventually led to it winning the contest between the two. I hear that there are still PBEM's going on (specially in the world of Star Trek Sims) but for the most part the utility and usability of message boards have come to dominate the online gaming community. Having done my fair share of PBP gaming I have come to believe their are certain advantages and disadvantages when compared to a table top game.
The main advantage PBP games have compared to table tops is that you don't have to work around the schedules of five people. You can log into the message boards whenever you have time, enter a quick post, and you are done for the day. Another strong advantage of play by post gaming is that it allows those of us who really like to write and develop characters a place to do so. In fact, if you want to really get an epic storyline going, I would strongly suggest PBP games.
The disadvantages of PBP gaming is the fact that there are no smiling faces at the table with you. You don't get the same feel that the table top experience provides. Also, if you are not much for writing or you don't have internet access it can be very difficult to actually do play by post gaming. Finally there is the fact that you never really know if anyone is cheating or not.
In the end, I find that there are times I want to use play by post for gaming and other times when I want the table top experience. I am glad that both are available to me and can't wait to see a time when technology allows us to get the best out of both worlds (and no WoW is not it)
If you are interested in gaming in a play by post game you should check out mythweavers.