In media today, it's common to talk about three screens: Desktop, mobile and TV. Many people watch TV on the first two now, and tools like Google TV and the old WebTV try to bring interactive, internet style content to the TV. People like to call the desktop the "lean forward" screen where you use a keyboard and have lots of interactivity, while the TV is the "lean back" couch-potato screen. The tablet is also distinguishing itself a bit from the small screen normally found in mobile.
More and more people also find great value in having an always-on screen where they can go to quickly ask questions or do tasks like E-mail.
I forecast we will soon see the development of a "fourth screen" which is a mostly-always-on wall panel meant to be used with almost no interaction at all. It's not a thing to stare at like the TV (though it could turn into one) nor a thing to do interactive web sessions on. The goal is to have minimal UI and be a little bit psychic about what to show.
One could start by showing stuff that's always of use. The current weather forecast, for example, and selected unusual headlines. Whether each member of the household has new mail, and if it makes sense from a privacy standpoint, possibly summaries of that mail. Likewise the most recent status from feeds on twitter or Facebook or other streams. One could easily fill a screen with these things so you need a particularly good filter to find what's relevant. Upcoming calendar events (with warnings) also make sense.
Some things would show only when important. For example, when getting ready to go out, I almost always want to see the traffic map. Or rather, I want to see it if it has traffic jams on it, no need to show it when it's green -- if it's not showing I know all is good. I may not need to see the weather if it's forecast sunny either. Or if it's raining right now. But if it's clear now and going to rain later I want to see that. Many city transit systems have a site that tracks when the next bus or train will come to my stop -- I want to see that, and perhaps at morning commute time even get an audio alert if something unusual is up or if I need to leave right now to catch the street car. A view from the security camera at the door should only show if somebody is at the door.
There are so many things I want to see that we will need some UI for the less popular ones. But it should be a simple UI, with no need to find a remote (though if I have a remote -- any remote -- it should be able to use it.) Speech commands would be good to temporarily see other screens and modes. A webcam (and eventually Kinect style sensor) for gestural UI would be nice, letting me swipe or wave to get other screens.