Well, to start, why do you want to learn C now? What plat are you developing on? What applications for it are you looking at? C++ mostly replaced C except for some things, like the Linux kernel.
For business type apps, which I work in, and which, from my observations, most of the jobs in the US are in, it is mostly C# (and other .net langs, like, ughhh, VB.NET) and java.
C is a very, very low level language. I would place C about a level above asm. Very few people do C aside from very specialized things like kernels and drivers. C++ is a step above that, but C++ has it’s performance drawbacks for things like kernels and drivers.
I mostly do windows development. I have not done a pure C commercial project since DOS. C++ pops up on occasion. Now, most of the game is C# and java.