Greenspun's Tenth Rule of Programming: any sufficiently complicated C or Fortran program contains an ad hoc informally-specified bug-ridden slow implementation of half of Common Lisp.
Pretty much everything on the web uses those two things: C and UNIX. The browsers are written in C. The UNIX kernel - that pretty much the entire Internet runs on - is written in C.
For infrastructure technology, C will be hard to displace.
The central problem of C and C++ is that they require programmers to do their own memory management
C is declining somewhat in usage compared to C++, and maybe Java, but perhaps even more compared to higher-level scripting languages. It's still fairly strong for the basic system-type things.
My favorite programming languages are Lisp and C. However, since around 1992 I have worked mainly on free software activism, which means I am too busy to do much programming. Around 2008 I stopped doing programming projects.
Of course, C proved indispensible to the developers of all its alternatives. Dig down through enough implementation layers under any of the other languages surveyed here and you will find a core implemented in pure, portable C
C is peculiar in a lot of ways, but it, like many other successful things, has a certain unity of approach that stems from development in a small group.
Web servers are written in C, and if they're not, they're written in Java or C++, which are C derivatives, or Python or Ruby, which are implemented in C.
No one wants one language. There are applications when it's appropriate to write something in C rather than in Java. If you want to write something where performance is much more important than extensibility, then you might want to choose C rather than Java.
C is a razor-sharp tool, with which one can create an elegant and efficient program or a bloody mess.
C makes it easy to shoot yourself in the foot; C++ makes it harder, but when you do it blows your whole leg off.