I think there is a lot of untapped potential for online games. I mean something else altogether.
Most online games right now are perfect simulations, or rather they attempt to be. Most online games imply multiplayer. Each player connected to the same server will be a part of the same virtual world. What player A sees going on is very close to what player B sees (albeit from a different perspective).
Let's break that constraint. Suppose there is an online multiplayer game where two players are connected to the same server, yet they live and interact in two completely different realities. Think about the doors this opens. The opportunities are endless. However, not many of them would make fun games. But I believe there may be something worthwhile out there. We just have to explore this direction a bit.
There already are some examples of this situation happening. Take a RTS game that is peer-to-peer. Imagine for some reason the two players go out of sync. At this point, they may both think they are winning the battle. There will be two winners and no losers, and each may have a lot of fun... until they realize their games are not in sync (via talking), where that fun will quickly end and frustration will set in.
But that's only an example of a broken simulation. The multiplayer RTS game was designed to be in sync, not out.
Let's look at online games that were designed to be not in sync.
I remember in a multiplayer FPS America's Army, there were 2 teams of players fighting each other. The game was made so that whichever team you picked, it would appear as the "good guys" and the other team is the "terrorists." This is a very minor visual aspect that has no gameplay value whatsoever. Maybe it wasn't even worth mentioning. ;)
As all good writers do, I'm leaving the best example for the last. There is a short simple indie game called 4 Minutes and 33 Seconds of Uniqueness. Assuming you don't mind the following spoiler, the game objective is simply to be the only player in the world playing it for 4 minutes and 33 seconds. It's a simple as that. But it is a great example of a game with online capabilities that does not attempt to simulate the same reality for multiple players at the same time.
What else is possible out there? I hope we are yet to find out.