I've been playing online games some over the last few days. A frustrating amount of time is spent trying to find games rather than playing them. A hotornot-style interface, in which the server guesses which people you'd like to play against and asks a yes/no as to whether you'd like to play them would be a vast improvement. There are several algorithms which could be used to determine selections and decide when a match happens. It's an interesting problem.
Also lacking are personalized thumbnail images like are used on livejournal and some chat sites. The more serious online communities tend to look down on images, due to the 'asl' banter flavor of them, which is unfortunate, since context greatly improves social interaction.
None of the online game sites I've used have an option for the players to replay a game and comment on it after it's done. This is one of the more social aspects of playing over the board gaming; it would be a nice addition.
Another missing feature is an integrated opening book which automatically displays your comments on the current position as play unfolds. Opening books are often viewed as cheating, but if everyone had them it would be fair, and rote memorization isn't a fundamental aspect of most games.