An "invite player" feature.
You can /invite anyone to any game you are currently in(be it you joined or created it). The invite option would be located on your profile. So if you click on someone's name, you see their wall, their medals, you can send them a private message etc etc... There will also be a "Invite to Game" button. Click on this, and a list of games you are currently part of that are not full will pop up. Click one of the games and wallah! They are invited to join the game. A PM will be sent to that player telling them they are invited to join the game you're in. They can of course decline ;p
Also, the would be an official invite, which means no password would be needed to join your game. So you can create a private game and then invite a bunch of people without the added difficulty of passing around a password and having to make sure everything is set.
Also, perhaps add the /invite feature to the options when creating a game. So when you create a game, you can type in a person's name and they will be sent an invite.
Lastly, another option would be to make the second part of this feature(the part after you click the person's name, where it shows you the available games you are in to send invites), a CHECK MARK menu, so you could potentially /invite someone to multiple games.
This will improve the following aspects of the site:
Save time for people searching for your games, also, you'll be able to create games on the fly and /invite people. Also, when playing multiple games with people, you can /invite people to multiple games all at once instead of PMing them a list of game numbers and passwords to join!