Mozilla Labs has a design challenge to encourage students to answer this question. In their own words:
As the Web becomes even more ubiquitous, we’ll never have to leave it. Whether it’s on touch tables, giant wall-sized screens, mobile devices, or just our computers, exploring the interactions for browsing a windowless Web will become ever-more important in the next couple of years.
To get started, you’ll need to submit a mockup of your idea. This can be anything from a napkin drawing, to a wireframe, to a polished graphic or video.
Unfortunately the deadline for the initial phase is only 3 days away, on March 1st!