I went to a talk by an Intel engineer saying this very thing. Fortunately it's not dead, and Intel has done more than anyone else to keep it from dying!!!
OTOH back about three decades ago I attended a talk by a Verbatim marketing guy (they built floppy disks) that predicted that magnetic bubble memories would soon kill floppies.
Well, he was right that floppies would die. But so did bubble memory.
When it does end, we will move onto other forms of computing, memristor based, graphene, photonic/optical, quantum (only really useful for some classes of problems), spintronics and such. Might have a bit of a dip off during the change over but then it will be business as usual.
We could start to see computers with more and more processors in them. The cost of producing a processor should continue to drop. Energy efficiency, (reduced heat) and cooling improved systems will keep being developed. So maybe we will end up with computers that are almost a solid mass of processors. That scalability isn't fantastic though, but it would work for maybe 10 years. Things like FPGA coprocessors could also help.
Finally we can look at breaking away from the current paradigms of computer science into esoteric things like biological/dna computing.
Most desktop systems are as fast as most people will ever need them. Remember now days all they are doing is opening a webbrowser and going to Facebook. The UI's keep getting more and more simplified.
Graphics in games is about the most demanding thing that happens on a desktop, which will likely keep going for some time until we have photo-realistic, realtime raytracing at retina DPIs on large screens, in 3D (maybe with voxels for some kind of future volumetric display).
Part of me will be happy when G.E. Moore (George) get's a little more attention.
One almost down I'm sure the I/O system will reach a wall soon as well. Only thing left is to optimize the software.
Time will tell.