What are common applications for C/C++? Can C++ be used for the same
kind of applications as COBOL?

Common Applications for C/C++? You're kidding, right? Nope, it's worth
$8 for you to find out, so let's start with, oh, I don't know, Unix,
Linux, FreeBSD, and practically every piece of software written to be
compiled. I'm exaggerating. Of course there are other languages, but
I'd hazard a guess that of compiled languages, few are more used in
new programs than C/C++.

http://www.dedasys.com/articles/language_popularity.html
http://www.cs.berkeley.edu/~flab/languages.html
Based upon the Sourceforge graphs, you can see that about 40% of the
projects are C or C++ (this is some 27000+ projects).

To answer your question: Yes, C++ can be used for the same kind of
applications as COBOL. The difference is that COBOL is designed for a
human to read and understand the source code, while C++ is designed
for the computer to read and understand the source code. At least,
that's the idea, anyway. It's possible to have human understandable C
and horrible COBOL.

This is a free comment.

There are many computer programming languages, of course. 
Historically two of the most important were COBOL for business
applications and Fortran for scientific or engineering applications.

As a crude approximation, I'd say that C/C++ became the language of
choice for writing new scientific/engineering applications, and
(various flavors of) Basic became the lowest common denominator for
business applications.

But from the inception of C, a design goal was portability of
compilers, libraries, and hence applications.  By combining efficient
performance with portability, the C/C++ implementations have staked
out a very broad range of uses.

Today's application programmers are often called upon to develop
software for cooperative-computing platforms (eg. the Web) rather than
for standalone platforms.  The lessons learned from C++ classes and
interfaces have had a big influence on emerging standards for these
new platforms.

regards, mathtalk-ga