One thing that's really helpful for asynchronous online gaming is a system that allows players to (tentatively) take ownership of the entire world, not just their own character. If there's going to be a lag between player post and GM response, a system with a focus on collaborative storytelling that allows the player to write a paragraph detailing an entire interaction between the player and an NPC, subject to veto or alteration by the GM, is going to move things quickly.
Systems with a "one turn = one player action" focus are likely to bog down if they get into:
"I sneak down the hallway." (a few hours pass)
"OK, you're at the end of the hallway." (a few hours pas)
"I quietly open the door." (a few hours pass)
"You hear a deep male voice yell 'Hey!'"
The more you can handle in a single transaction:
"I sneak down the hallway and quietly open the door. Someone notices me and yells, but I duck inside before they can identify me and hide under the desk for a moment. I hear them running off to raise the alarm, and quickly find the documents in the desk. I rush out the door and down the hall just as they return with a guard, and they give chase." (a few hours pass)
"You retrieve the documents, but when you try to leave, you find that whoever saw you must have magically sealed the door shut before they went for help. As you struggle with the door, you hear armored footsteps pounding down the hall outside - there are two guards coming down the hall in the company of the mage who noticed you..."
The more you can handle in a single "action," the smoother things will be - but generally, handling more in one action means giving up some control over the world to the players. It helps to have players who are willing to write negative outcomes as well as positive ones, or a system that takes it into account by making partial successes more likely than absolute successes.