THIS IS AN UP TO DATE ANSWER FOR WINDOWS USERS - VERY SIMPLE SOLUTION.
As pointed out by other, the problem is that python/cython etc. tries to find the same compiler they were built from, but this compiler does not exist on the computer. Most of the time, this compiler is a version of visual studio (2008, 2010 or 2013), but either such a compiler is not installed, or a newer version is installed and the system prevents from installing an older one. So, the solution is simple:
1) look at C:\Program Files (x86) and see if there is an installed version of Microsoft visual studio, and if it is newer than the version from which Python has been built. If not, install(/update to) the version from which Python has been built (see previous answers), or even a newest version and follow the next step.
2)If a newest version of Microsoft visual studio is already installed, we have to make Python/cython etc. believe that it is the version from which it has been built. And this is very simple: go to the the system environment variables and create the following variables, if they do not exist:
VS100COMNTOOLS
VS110COMNTOOLS
VS120COMNTOOLS
VS140COMNTOOLS
And set the field of these variables to
"C:\Program Files (x86)\Microsoft Visual Studio 10.0\Common7\Tools" (if visual studio 2008 is installed), or
"C:\Program Files (x86)\Microsoft Visual Studio 11.0\Common7\Tools" (if visual studio 2010 is installed) or
"C:\Program Files (x86)\Microsoft Visual Studio 12.0\Common7\Tools" (if visual studio 2013 is installed) or
"C:\Program Files (x86)\Microsoft Visual Studio 14.0\Common7\Tools" (if visual studio 2015 is installed).
This solution works for 32 bit versions of python. It may also work for 64 bit version but I've not tested; most probably, for 64 bit versions, the following additional steps must be performed:
3)add the path "C:\Program Files (x86)\Microsoft Visual Studio 11.0\VC" to the %PATH% environment variable (change the number of the version of visual studio according to you version).
4) from the command line, run "vcvarsall.bat x86_amd64"
That's all.