Well now we have Tablet PCs. 122dpi screens. Nowhere near my number, but it looks like I could be wrong:
Electronic printers operate from 300 to 1,200 pixels per inch, but displays do not need as much resolution because they can be gray scale devices. For example, a color ink-jet printer never prints more than two colors at a given pixel location. A 200-dpi high-density display that has full color (red-green-blue, or RGB) would be equivalent to a 692-dpi printer. The real resolution for LCD screens is about 3.5 times higher because it uses RGB subpixels where white is actually an optical illusion. This, combined with the higher density of pixels, improves jagged line reduction. Thus, text readability is closer to paper quality. People can even read novels on LCDs without eye strain.
(from an article in MSDN on Tablet PC software development)
So maybe I only need 200dpi? OK, cool, so we're looking closer. But Tablet PC are far too expensive ($5000) and too big (A4 sized), but I could live with A4 I suppose, although I'm mainly going to want to be playing music on it and taking notes. A4 is hard to drag around with you. Paper back book sized would fit in a large pocket.