As systems become more robust and reliable and they learn to deal with dispersed syntax, differences in language and body language the answer is there will be no personal computer as you see it today with an OS as you see it today. There will be bits and pieces everywhere either interconnecting wirelessly to share tasks or taking commands verbally and perhaps even emotionally. Verbally is obvious, but for example on the latter: you walk into your kitchen slightly depressed and your computer recognizes the signs and pours you a cup of hot cocoa with itsy bitsy marshmallows (or whatever you drink), starts your hot bubble bath and instructs the house "robot" (for lack of a better word) to add your favorite toy battleship to the bath because that's what you usually drink and then do when you "look that way".
BlackBerry and iPod are examples of the other half of what I am talking about. They link to systems out on the Internet that you could just as easily connect to with your "application" device, which brings us back to the original question of "what will the OS look like". For other than developers of the systems, the need for an OS based general purpose computer will lessen to the point of non-existence and they won't care if it's based off a Microsoft, UNIX (or UNIX derivative), VAX VMS, Palm, DOS, or any other operating system. To them it will be like magic.
That finally leads to the developers of these systems. Allowing for the original hypothesis that the general-purpose computer will become less and less important, thereby upgradeable embedded OS systems will become more and more prevalent. My personal opinion is the Palm Life Drive or Treo 650 is somewhat representative of what that general-purpose system and OS is going to look like.
In other words I think people are going to essentially carry a hard drive or memory stick that contains all their defined life data. It could simply be their watch or a piece of jewelry or something else like it, but that's the general idea.
If the user needs to do something that requires a personal computer like we do today (i.e. the use of voice commands are not good enough for whatever the task at hand is) when they get close enough to something equivalent to today's dumb terminal, they will instruct their item to basically "log into" the keyboard, mouse and monitor so they can then use some application. That application can be either from that item in part/whole or in part/whole from the Internet.
The OS, in this hypothesis, ultimatly becomes nothing more than hardware drivers, handshaking and security protocols.