From my own personal experience:
I don't know how many job listings explicitly call for a "C programmer", but as Mario F. said, there are definitely niche markets that require this knowledge.
For myself, I develop code for embedded devices - but I also design the hardware that these chips will run on. Since the complexity of the software is fairly simple, relative to the complexity of writing computer applications, this likely falls more into an engineering toolset, rather than a programming toolset.
Also, not a lot of compilers for these devices support C++ (although this support is steadily increasing of late).
These two factors give me a preference for the C language. I'd prefer less abstraction and a lower level of control to help ensure my circuitry plays nicely with the code in the device.
This relates to my "professional" interest in programming. I also have a "hobby" interest in programming, for which I also prefer C. But this is mostly for subjective reasons, rather than objective.
So in short - you probably won't find much of a demand for C programmers in computer software development (though I don't know this for a fact), but there are definitely places where the usage of C is still alive and well (much to the chagrin of some of our more vocal critics of C on these forums).