I recently had to upgrade my TV due to the fact that here in Australia digital TV is replacing the old analogue system. A side effect of this was that my new TV can connect to the internet. I was curious about this so I grab a long 3 metre network cable and plugged it into my modem router and then into the TV. The TV immediately picked up that I was connected. I then fiddled around and managed to look at web sites and use a Twitter widget. This TV also comes with Skype installed but you need a specific web cam from Sony before you can use it.
You can now start to see the convergence between equipment like Tvs and the internet. I am still unsure if you would want to be interrupted with a skype call while watching TV but the possibilities for internet convergence are endless. I have included a pic showing my website on TV apologies for the blurry image that was me not the TV.