This is very cool Matt. I will add a little to it. My experiences are based on playing varius games with narrative mechanics or free form games, not PBEM as such.
I'll stick to some techniques and pointers I've learned by now:
A) Say "yes, and..."
When building on the shared story, accept other's contributions and build on them. Almost never annul or veto anything. If someone describes an action where your character is thrown on the ground, do not say "no, he can't do that, he would not fall". Instead describe how you roll with the fall and swiftly regain your feet, or how you from you new position sweep at his legs and pull him down as well.
Of course, if something does violate your limits for your character, your comfort zone, then saying "I'm not ok with this" is fine and should, IMO, be respected. Just make sure your limits aren't "if my character appears less than perfect". Also, sometimes the GM or the rulesystem does things we do not like, then it is almost always better to just roll with it.
B) Pass the ball
This is mostly the same as Matt's point #3. Try to intentionally make your descriptions incomplete, so others can use what you left unfinished to build their contribution. For example, in a duel I might write that "The countess makes a feint at you, but overextends and has left her side clearly exposed..." the intention is clearly that my the player of my character's opponent can build on this. This can be applied to many other situations, like warfare and conversations. Leave some blanks for others to fill.
C) Unimportant bystanders and participants are good tools for dramatic action
If you are describing someone fighting a unit of soldiers, then killing a few soldiers is a good way to provide some action and make your character look cool. Especially in action scenes, there will often be a primary opponent (the villain) and his minions. Kill a few of them, hell have a few of them jump out (there is always another ninja behind the door), just do not describe your character sending all of his minions running, as that changes the situation too much. The same can be applied in other situations - like in a court. Have someone shout from the sidelines, only to be shut down by a few well-placed words.
D) When in doubt, take a hit
If you're in doubt as to what to write for your character, especially in action scenes, the easiest trick is to describe your character taking a minor injury or some kind of setback. Describe how he stumbles and falls, then describe how he gets up again or turns it to an advantage. In almost all action movies the main character always takes a terrible beating (Die Hard I, anyone?), then gets up and does the job. It is a good way to raise tension and to make characters look tough - or to make them look human and mortal, depending on the situation. Again, it can be used outside of actionscenes - having your character fume in anger, to look at a loss, etc.
E) Be careful with headspace
Describing why your character does something or what he is thinking is a cool way to add something to the narrative. I like it myself. However, it should always be clear what part of your description is visible to others - that way the other players know what they can have their characters act on. Use a different font or something for "thought bubbles", make it clear. It should also be used in moderation, the focus should be on what those who are together with or close to your character can perceive.