While streaming video is no problem (doesn't matter if you're watching YouTube or game feed), control latency is. Input from your controls will have to travel to remote location and then back with video.
Latency is enough of a problem in network games - each realtime multiplayer game has to predict what other players do at this very millisecond, and then deal with conflicts if the prediction was not accurate (this results in, for example, one player being killed after he ducked into cover, because for a second played he was still vulnerable).
Now imagine all of your input having a delay of 100-200-300 milliseconds. While there will not be conflicts (it is just you and the game), imagine racing or shooting or playing Super Mario with such delays!
So, realistically remote gaming is limited to local network, like mentioned Steam streaming.