I use a modified version of the Hero Point rules. They are similar to what's available on the SRD with some tweeks to ease use in PbP format and remove ambiguity where possible.
A character can have a number of hero points equal to half his or her character level (round up) at any given time. Any points gained in excess of this are lost. Characters begin the game with 1 hero point, and only gain them when handed out by the GM (you don't gain a point when you level).
Gaining Hero Points
Campaign Arcs: When a major story event has been resolved each PC will receive a point. You can assume this will be roughly 1 point per "book" of an AP, with one or two additional points scattered through the campaign.
Character Goal: Relating to your campaign traits, each character will have a number of personal story events, that upon resolution will earn the PC a Hero Point.
Intrusions: Taking a concept from Numenera, the majority of Hero Points a PC receives will be through GM Intrusions. An intrusion will generally be presented as an option for a specific PC. The Intrusion will always be a complication to the situation the PC is in, and the option will be to either accept the complication and receive a Hero Point, or to deny the event and spend a hero point.
The specific event/complication will always be a hindrance but will almost always involve a check of some sort to either get through unscathed or lessen the effect. It will never be outright fatal.
For example, you might be walking down a dungeon corridor and receive the following message...
GM Intrusion
A panel in the floor under you gives out, dropping you into the darkness. If you accept the Intrusion gain a Hero Point and make an Acrobatics check. If you deny then spend a Hero Point and nothing happens.
The Acrobatics check is to see if you lower the damage from falling into the pit, which would likely be a matter of 2d6, half if you make the check at DC 15. If you refuse the Intrusion in this instance then essentially there really was no trap there and the floor is solid.
Beyond handing out Hero Points and complicating your lives, Intrusions serve another purpose. Adding to the story. For example, in the above Intrusion the pit you find yourself isn't just a twenty foot deep hole, but a way into another level of the dungeon, perhaps less explored and looted than the rest.
Not all intrusions will add to the story in such a way. Sometimes it's just a way to make a given encounter more interesting.
Expect to see a fair number of intrusions. If we were playing in a table game rather than PbP you could expect to each encounter a personalized Intrusion per session at minimum, with a smattering of "random" intrusions.
Spending Hero Points
Bonus: You can spend a Hero Point before or after a d20 check. If used before a roll is made you a +8 luck bonus. If used after a roll is made, this bonus is reduced to +4. You can use a hero point to grant +3 to another character's d20 check after its been rolled, as long as you are in the same location and your character can reasonably affect the outcome of the roll (such as distracting a monster, shouting words of encouragement, or otherwise aiding another with the check).
Extra Action: You can spend a hero point on your turn to gain an additional standard or move action on your turn this round.
Reroll: You may spend a hero point to reroll any one d20 roll you just made. You must take the results of the second roll, even if it is worse.
Recall: You can spend a hero point to recall a non mythic spell you have already cast or to gain another use of a non mythic special ability that is otherwise limited by number of uses per day.
Cheat Death: A character can spend 2 hero points to cheat death. How this plays out is up to the GM, but generally the character is left alive, with negative hit points but stable. For example, a character is about to be slain by a critical hit from an arrow. If the character spends 2 hero points, the GM decides that the arrow pierced the character’s holy symbol, reducing the damage enough to prevent him from being killed, and that he made his stabilization roll at the end of his turn. Cheating death is the only way for a character to spend more than 1 hero point in a turn. The character can spend hero points in this way to prevent the death of a familiar, animal companion, eidolon, or special mount. You may spend 3 hero points to use Cheat Death on another PC or NPC (including Cohorts).