As much as I an enthusiast for mobile technology I've maintained that people espousing the idea that the PC is dead are dead wrong.
It doesn't get the press and is as unsexy as could be, as it is a technology rooted in the days before it was hip to be square, but the venerable mainframe not only continues to chug along, but is quietly the foundational technology for many large corporations and government agencies. IBM continues a brisk business in mainframe sales and COBOL programmers command an enviable income not just maintaining but actually growing the massive base of COBOL code. And perhaps embarisingly, mainframes are still king when it comes to mission critical 24x7 reliability.
That being said PCs surely have entrenched themselves deeper and more widely than any mainframe. And the PC is dead? I don't think so. I'd dare submit that nobody reading this in 2012 will see the death of the PC (nor the mainframe for that matter).
Now the PC as a consumer product? A case can definitely be made for that market diminishing to a niche. Personally its still my favorite gaming platform and I hope that never goes away.
For business it will certainly diminish as an end user device as mobile penetrates particularly as a replacement for laptops. The larger laptops will become as quaint as those early "mobile" computers from the 80s. Where desktops have not been replaced by laptops there likely will be where PCs remain for the long term. I would include workstations, CAD/CAM, software development (although I've written more than a few lines of code on my tablet), and more. Of course servers but that doesn't need to be said.
Still mobile, combined with cloud services run on PC technology, will continue to grow as the greatest informational revolution in human history with far reaching consequences many as of yet not dreamed.
P.S. I actually was required to take COBOL in college for my MIS degree. I was probably in the last 2 or 3 classes that had to.