Since no genre was even specified, these responses will be all over the place. Perhaps too chaotic.
1) Have the entire world run on AI. When the players jump in, the take over the role of an existing AI NPC, making them their own. This allows for a world where you never know if someone is real or not, unless they chat with you, or they are on your friends list and are flagged. You can join a team waiting to go on a quest, and not know if your team mates are AI or real. If someone drops out, their character continues.
2) Obvious list: Head to Head competition, Team vs Team competition, Leader Boards, chat
3) Buff's (DND mini game on facebook, uses the concept that players currently online (and on friends lists) can 'buff' each other, or give temporary boosts)
4) Team Strategy. I.E. Maze Game. Each player is on their own, but feeding each other information about the environment.
5) Team Points. What ever game, each player gets a free amount of points per amount of time. They get a buffer. They can spend these points on extra magic, or dropping things into the game to help them. If one player doesn't do anything with their points for a while, and it reaches say 100, immediately 25 points go to a Team Pool. and the player goes to 75. This allows team members to agree to hold off on useing team magic until they can afford a larger spell or something, or if a player goes off line while the team is still active, that they are still contributing some how.
6) Face Mapping. Have a 3D character, Have a video camera. Setup an app that automatically uploads a image of your face (automatically cleaned of background) ever 500ms or so. HAve the game keep mapping that image as the face of your 3D character online. the closer a character is, the more often it will update. That way you can see the real expressions, etc...
6b) same thing, but have the app map the expression, and simple change an expression on an existing face. I think it would be interesting to see the expression change to confident, alarmed, distracted, excited, etc... mid game play. Much of real life game play happens in the facial expression and body signals. It would be interesting to have this carry over into the game.
7) Voice controlled AI Team members. Have an open chat between members on a team. Include AI members of the team. Include voice recognition. When a player speaks the name of an AI team member, they can follow it with certain commands or suggestions, and the AI team player will comply. (depending on your rank in the team, and what other requests were sent to them.)
8) Interactive Ghost Review. Similar to Starcrafts replay of entire games with full clarity, Having a replay, except for a 3D RPG style, where you can walk around as a "ghost" character in the world, with another party member, and replay/rewind etc.. Presented as magic and a form of training. Like an AI instructor who teaches you battle strategy. But with multiple players walking around. Even allow them to be in different times. By showing all "ghosts" as transparent, and if they are not in the same moment as you, it shows as a bar over their head indicating forward or backward, and you can click them to see what they see.
- It puts an interesting time element into the game.