MinGW GCC -- Single 32-bit and 64-bit cross-compiler?
AFAIK mingw targets either 32 bit windows or 64 bit windows, but not both, so you would need two installs. And the latter is still considered beta.
For you what you want is either mingw-w64-bin_i686-mingw or mingw-w64-bin_i686-cygwin if you want to compile for windows 64. For win32, just use what you get with mingw-get-inst.
See http://sourceforge.net/apps/trac/mingw-w64/wiki/download%20filename%20structure for an explanation of file names.
I realize this is an old question. However it's linked to the many times the question has been repeated.
I have found, after lots of research that, by now, years later, both compilers are commonly installed by default when installing mingw from your repository (i.e. synaptic).
You can check and verify by running Linux's locate command:
$ locate -r "mingw32.*[cg]++$"
On my Ubuntu (13.10) install I have by default the following compilers to choose from... found by issuing the locate command.
/usr/bin/amd64-mingw32msvc-c++
/usr/bin/amd64-mingw32msvc-g++
/usr/bin/i586-mingw32msvc-c++
/usr/bin/i586-mingw32msvc-g++
/usr/bin/i686-w64-mingw32-c++
/usr/bin/i686-w64-mingw32-g++
/usr/bin/x86_64-w64-mingw32-c++
/usr/bin/x86_64-w64-mingw32-g++
Finally, the least you'd have to do on many systems is run:
$ sudo apt-get install gcc-mingw32
I hope the many links to this page can spare a lot of programmers some search time.