I'm a very old dog (still learning new tricks). I started on mainframes, migrated to client/server and desktop, and lately Internet programming. With the language skills you've mentioned having and the current state of the programing universe, I'd say the main (maybe only) virtue of learning a compiled language such a C/C++ would be getting a wider view of how languages work. This isn't a bad thing, but I wouldn't make it a high priority to do desktop programming. Learn Java for the same value and the portability (write-one-run-anywhere). Learn Python, Ruby, Perl...any of the other web-oriented languages.
You said you already know CSS, HTML, JavaScript, PHP....really? Do you write standards-compliant CSS and HTML that address accessibility issues and ALWAYS validate under the W3C requirements? Do you consistently apply semantic markup and include good SEO as part of the development process? In JavaScript, do you use OO principles...how about in PHP? My point is that it's better to be very good at a smaller set of skills than a "Jack of all trades, master of none."
Learning other languages can expand your understanding of the general, theoretical principles that underpin programming as an art and science. In varying degrees of expertise, I know APL, BASIC, C/C++, FORTRAN, Java, JavaScript, PHP, PL/1, and SQL as well as CSS, HTML, and XML. I've written specialty languages, using the Interpreter design pattern. However, I learned those topics to pay my bills; that is, somebody paid me to solve their problems, using those tools. Unless you already have a paying customer for a new language, polish what you already have and extend your new learning in the arena of your current expertise, i.e., web programming.
Study the theory of programming, e.g., Functional Programming, Object Oriented Programming, Design Patterns, etc., and devote effort to learning how to design and tune relational databases - that's a better investment than just haphazardly picking up another language without a goal or a paycheck to motivate the choice.