One day we'll all be reading e-papers: Virtually the only thing left separating old media and new media is the medium itself - the fact that the web (generally) exists on PC-type devices with mice and keyboards and huge monitors while print media (generally) exists only on pieces of paper that you can flick through. Not that these differences aren't hugely important - you can't very easily search a print magazine by keyword or click on a picture for more information, and it's still a bit risky trying to surf the web in the bath.
But as soon as a compromise can be found - the moment someone invents a decent lightweight, ultra-thin electronic reader that looks and feels like a newspaper or a magazine but allows us to access electronic content on the move - there will be nothing to stop the total convergence of the two media.