Forum games are my one true weakness.
"Let's tell a story" and "Counting to One Million" are classics, and would be nice.
...'Posts cannot contain letters from your username' is pretty fun.
I've always thought making a 'spoiler maze' would be interesting. But I'm on mobile and an example would take a while, so yea.
'Last person to post wins'
Leave out (roughly) half of your sentance. The person after fills it in, and starts another.
Uh.
"What kind of person would the person above you kill/sleep with/whatever?"
This one might be a little too complicated, but it can't hurt to mention :
"Let's adventure!". It's kind of like those text-based DOS games, if the interpreter was drunk.
The first post is "You are standing in front of two doors. Do you take the left, or right?"
The next would be "Left. This room is full of money. How much do you take?"
"Ten billion. You buy an island and retire!"
"Pirates invade your island. You die."
Once we die, the game restarts at wherever OP began.
(Each post must contain an action first and an instance second.)
Start with sentance X, turn it into sentance Y. You can only change one word.
That's probably enough. I might edit this post later with more ideas.