I know there are a lot of gamers who play online, using forums, Google+ hangouts, Roll20, or IRC/other text chat, so I figured I'd write up a few thoughts on the pros and cons of Play-by-Post (PbP) gaming. I'll also post some advice I have for playing PbP games.
Pros1. Preparing for a PbP game isn't as intensive on the GM. You may not have less stuff to do as a PbP GM, but due to the pace of most games, you've got more time to do it. Things take more time in PbP, especially when you may only get one post a day from each player, which gives the GM more time to prepare.
2. It's much, much easier to improvise. Because of the time factor, if the PCs do something unexpected, it's usually totally fine for the GM to sleep on it rather than make an immediate decision. This generally leads to decisions and rulings that are more thought out.
3. No more worries about stopping play to look up a rule. The GM (and generally, all the players) have plenty of time between posts to look up a rule or create a suitable house-rule, in contrast to a face-to-face or real-time online game where you'd have to interrupt play to search through books and PDFs.
4. It's much less time-intensive. As a GM, the longest I've ever spent on a post was thirty minutes for a game-opening post, which I consider to be prep rather than active play. The longest I've spent on an active play post (combat, roleplaying, etc.) was about fifteen minutes where I was responding to multiple players at the same time. As a player, even with combat actions, I haven't spend more than five minutes or so on a post.
5. Scheduling isn't a problem. If all the players and GM have time for one post per day, there's almost no time taken out of everyone's daily schedule. It's much easier than setting aside three or four hours every week for five or six people to get together and play.
Cons1. PbP is slow. Really slow. Like, one combat in Dark Dungeons can take four days to play out. That kind of slow. In a 4E game, one combat can take upwards of a week or so.
2. Player/GM interest can wane rapidly. Between the slow pace and waiting on everyone else to post, it can be really easy for a player or GM to just lose interest in a game. I always take an extra two or so players when I do my game recruiting to combat player drop-out.
3. Games die very easily. Sometimes it's a GM losing interest, sometimes it's multiple players, and sometimes it's something as simple as the GM or a couple players taking a break for a couple days (holidays, vacation, whatever reason) for a game to go on hiatus and just never come back.
AdviceMost of my advice for PbP gaming is similar to what I'd give for a regular game, with a couple PbP-specific additions. Remember, this is what works for me and is mostly focused on OSR games. Take it with a grain of salt, your mileage may vary, etc.
1. As a player, get involved. Offer to help keep the game wiki updated, offer to help map dungeons, whatever you need to do to keep interested. The more you invest in a game, the more you'll want to keep playing.
2. Let the GM make all dice rolls. It speeds the game way up and simplifies things, especially for combat. A three- or four-post back and forth discussion between the GM and a player on what dice need rolled, especially for situations where success or failure will lead to another roll, is much more time-consuming than a player including a request for a die roll in their post and the GM making that roll and any related rolls and including the results of the roll(s) in their next post.
3. Give out XP boosts. For OSR games, give out a lot of XP. Advancement in certain games takes a really long time, and in PbP, that time is even longer. To mitigate that, give out extra XP, either through story awards (The party helped the kobolds achieve a common goal instead of murdering them? Here's some extra XP!) or reaching certain goals (The group survived the dragon attack with no deaths? Everyone gets a 10% bonus on XP for that encounter.).
4. For GMs, either keep your posts short or format details using a list. People generally aren't going to want to read big blocks of text to try to find what's fluff and what's actually relevant detail. Instead of working details into a paragraph, put them in a list to make them immediately stand out and so the players know it's relevant information.
5. Have separate In-Character and Out-of-Character threads. IC threads are used for in-game roleplaying and relevant rolls. Out-of-Character threads are for anything else - metagame discussions, character build advice (if your game has character builds), brainstorming, etc.