The following is a bit of information about how I run PbP games.
I expect that players will be posting at least once a day, if not more frequently. Typically, I will use the "Rule of Three" - where if there is a non-combat decision to be made, I will move on to that when three people (or half) have agreed to go in a certain way.
In combat, I will be posting a "combat tracker". This will show who is up, and status of all combatants.
Generally speaking, if there are knowledge or other checks to be made, I will add the rolls to a post, spoilering the information that would be learned. Until proven otherwise, I assume that the players are adult enough not to mix "player knowledge" with "character knowledge".
The following PC rolls will always be made by me to keep things moving:
3. Sense motive
4. Saving throws
5. Group diplomacy*
Player dice rolls of these types will be ignored, unless specifically requested by me.
I may make the following where appropriate, but you may request to make these yourself (let me know if you prefer to roll these yourself):
Further, I may make a roll of any kind on your behalf if you do not post within the 24 hour time frame (see above for more on this).
* Where the group is involved in a diplomatic action and a diplomacy roll is required, I will roll using the PC with the highest modifier for the group as the primary roll and the next highest modifier for an assist. Depending upon role playing and other circumstances, I may allow multiple assists also, or require someone other than the PC with the highest modifier make the primary roll. Otherwise, the players roll these individually.
Finally, a convention I have adopted (mostly for rolling during combat) in PbP games that I run is as follows:
1. No rolls during combat for any checks that do not specifically require an action unless called for by the GM. Same for free actions that do not influence combat. Eg. Knowledge (dungeoneering) to identify that ooze is a free action, but this is a roll you must ask the GM to make for you (unless he has asked for it). Concentration check to cast a spell is a free action, but that's fine to roll yourself (since it forms part of your cast spell action). No trying to game the dice roller.
2. Always roll for actions in the order in which they occur. When in doubt, roll reactions to GM first, reactions to players next and then your actions. This should help minimize players swapping over save throws for attack rolls (and the like). Also roll your attacks in the same order each round, for example, no trying to swap the extra haste attack around in the order to get a better hit.
3. If you do want to make an "actionless" skill check, ask the GM to roll it for you. He'll have to post to tell you the results anyway.