There are even several frameworks for developing them, including Wt, cppcms, CSP, and others. FastCGI's mainline implementation is in C, and directly supports several languages, including C++.
Any programming language that can parse strings can be used in CGI or a servlet. Any language that can implement bindings with C libraries can also be used to develop modules for ISAPI- or Apache-compatible servers.
It's not particularly easy in C++, and good templating engines are few and far between, but it can be done.
Of course, the question of whether this is a good idea is another matter entirely. :)
Do note: Major websites like Amazon.com, eBay, and Google do use C++ for parts of their infrastructure. Realize, however, that Google only uses C++ for speed-critical systems, and Amazon.com only relatively recently switched away from Lisp (which angered some of their senior staff :).
Facebook formerly compiled PHP to C++, but their HipHop compiler (written partly in C++) has since been retooled as a bytecode virtual machine.