If history is any guide my little boy, who's now almost five, will have a personal petascale (petaflop performance with petabyte storage) computer before he graduates from University.
What do you think he's going to do with it?
My first thought on asking that question was along the lines of the idea that world computing needs could be met with no more than five mainframes, that Unix is a toy for geeks, and that no one would ever need more than 640K. My second, however, was that Dr. McCoy's tricorder would have to be a petascale device.
On the other hand we probably don't have to wait that long for our first run at a tricorder. For example, Apple has an opportunity to turn its pocket Mac (nka iPhone) into an open architecture device providing both communication-to-user and communication-to-network services for embedded "memory stick" sized devices. Combine what we could build now along those lines with fast enough access to a big enough, ubiquitous enough, network computing resource and the pretty girl you just met could be asking you to breath at her pMac - to get an instant analysis of your general health and what the combination of her genes with yours might produce.
Right now that combination: a handheld device interacting with a humongous distributed network computing resource, is so obviously a better a model than the personal computer that much of the progress between now and then may simply consist of getting it to work better: shrinking the bit we have to carry while growing the power of the network resource, and thus making the combination faster, better, cheaper - and more useful.
But you know what's wrong with that picture, right? Exactly, it's a five mainframes answer: projecting what we have now as the basis for guesses about future technologies no one's even invented a need for yet.
One thing I'd bet on is communication functions - non intrusive, real time, native speaker quality, multi-language translation. Beyond that, however, I certainly hope progress continues, but I don't know what he'll do with the thing - do you?