There are two C++ standard libraries supported by Apple compilers.
The default for 10.8 and earlier is libstdc++, supported by Apple GCC
compilers, GNU GCC compilers, and clang. This was marked deprecated with a
warning during compile as of Xcode 8.
The default for 10.9 is libc++, which is also the default for clang on older
platforms when building C++11 code.
There are subtle incompatibilities between several of the C++ standard libraries, so Homebrew will refuse to install software if a dependency was built with an incompatible C++ library. It's recommended that you install the dependency tree using a compatible compiler.
If you've upgraded to 10.9 from an earlier version - because the default C++ standard library is now libc++, you may not be able to build software using dependencies that you built on 10.8 or lower. If you're reading this page because you were directed here by a build error, you can most likely fix the issue if you reinstall all the dependencies of the package you're trying to build.
Example install using GCC 4.8: brew install DESIRED_FORMULA --cc=gcc-4.8.
Get GCC 4.8 via: brew install gcc48