*Edit* What Jim Said
+ though it's uncertain within what timeframe, there's a convergence starting to happen now, that all point to "your game on any device", along with connectivity of many types of devices to the TV.
Right now, for example, Apple has rentals and movie purchases that you can "shift" over to whatever device you want to view it on, be it your PC, Ipod Touch, Iphone, Ipad, or your television via AppleTV. Or for that matter there are cables to output video direct from your Iphone to a TV.
It won't be long before this is all wireless and has even less hoops to jump through (its pretty painless as it is, but annoying that a "rental" sits only on one device at a time).
The buzz in the games industry is about also moving in this direction. For example buying a game that can be played from wherever you happen to be. So, your Iphone while youre on the train, or then you get home, and play the same game on your PC (better graphics obviously) linked to an account that puts your score and progress to the exact same place, despite it being a different device.
Then there's digital delivery, which the game industry LOVES and looks forward to being a major solution to piracy (though as we all know, the crackers are not stupid and can find a way but at what cost to the game's features?)
As internet bandwidth increases (be it fibre optic service or 4G and 5G cell) there's also going to be the emergence of games rendered on the server and just streamed to you. You can see proofs of concept of this kind of thing already via "VNC" type applications that stream a render of a PC game to a handheld / cel phone. Just remember, whatever is crude and "too slow" now, will not be so in 10 years.