This is something I've thought a lot about as I've always been fascinated by what the future holds in different kinds of technology. I think the iPhone, along with other smartphones will eventually converge with and replace laptops, along with every other electronic device we may carry. We are already seeing smartphones with desktop-like computing specs of just a few years ago coming to market in the next year or two. In 15 to 20 years the computing power of your iPhone will make todays desktops look like Commodore 64's.
I think phones will stay about the size of a current iPhone, and be more of a personal notification/phone/navigator/augmented reality device while you're walking and driving. And for when you are sitting in class, at work, or wherever, and need a laptop type of device, the phone will have an expandable screen and keyboard. How this will be done I don't know, but I think that's where things will go. Maybe the phone will be able to project the screen and keyboard onto or above a table as some sort of 3D hologram and use similar technology that the Xbox kinect uses to read gestures and inputs to the keyboard and screen.
So once you sit down in class or at work, you set your phone down on the table, and you have a 15" virtual screen and keyboard in front of you, no docking it into anything, no bulky laptop to lug around. And of course this will do wonders for games!
I think things like augmented reality will really take off, instead of holding your little 3.5" screen phone to the sky to see the name of that bright star to the south with apps like Star Walk, you'll use the display to render pointers and names to the actual stars in the sky instead of just an animation. When you get lost from your friends at a concert, instead of trying to pinpoint their location from a sat image using an app like Loopt, you'll see a blinking red light over them in the crowd as you point your phone towards them. Or maybe it will point you towards the guy selling a ticket that you need that he just posted to Craigslist.
I also think they will become like a personal safety device, using location awareness (goodbye privacy) to alert us of dangers based on where we are. So if you go down to the beach, and lets say there's a tsunami warning, or high surf, your phone will alert you of the conditions. Same for if you are in the path of a tornado, instead of having to watch tv, or wait for tornado sirens, your phone will instantly alert you with a warning the second the weather service issues the warning.
The things that can be done with the technology by then will be pretty incredible, it will be interesting to see, that's for sure, and hopefully by then they fix the notification system! Wouldn't wanna miss that tornado warning because you just got a Holotime request from your girlfriend!