QEMU/MinGW

There are pre-compiled binaries for Windows. It may save some time to use them. However as of this writing, they are out of date with respect to the source repository, by a full version number.
Download the source code at the main website's download page.
Run ./configure from the directory where the source archive was extracted. This should automatically detect that your system is MinGW.
Dependencies - There are several libs required that may not be installed as of yet. If configure ends complaining that one of these is missing then follow those steps.
- zlib
  - Download the zlib source code into a different directory and
    - Run ./configure in that directory
    - Run make -f win32/Makefile.gcc
    - Run export LIBRARY_PATH=/usr/lib
    - Run export INCLUDE_PATH=/usr/include
    - Run export BINARY_PATH=/usr/bin
    - Run make install -f win32/Makefile.gcc
- gettext
  - Purportedly required for glib.
  - Download here.
  - Extract and run ./configure (this will take a while as it repeats many tests in each build subdirectory)
  - Run make.
  - If it fails with a syntax error at line 103 of test-lock.c, then change that function to return pthread_t instead of void* and remove the cast on the error line. Then run make again.
  - Once the build succeeds, run make install. It will install to /usr/local. Documentation and examples will be created for each existing language.
- libiconv
  - Purportedly required for glib.
  - Download at the project's homepage.
  - Run ./configure in the extraction directory. The same configuration script that was run so many times for configuration of gettext will be invoked many times now.
  - Run make.
  - Run make install.
- glib
  - Required for pkg-config.
  - Here is a page about compiling glib on MinGW. It mentions that gettext and libiconv are required.
  - The source can be obtained here.
  - Run ./configure in the extraction directory.
  - If it complains it can't find zlib, then follow the instructions at the French wiki and export CFLAGS and LDFLAGS. The values recommended may be wrong, these were used:
    - export LDFLAGS="-L/usr/local/lib -L/usr/lib"
    - export CFLAGS="-I/usr/include -I/usr/local/include"
    - Then you'll probably find that pkg-config is required to build glib.
    - There's a suggestion to use Cygwin to bootstrap the process by using its pkg-config and dll for MinGW. This probably makes sense to the people responsible for glib.
- pkg-config
  - You may or may not have gtk installed, and the FAQ at MinGW says at the moment that gtk is required to install pkg-config. This may or may not be installed along with GIMP, and MinGW may need to be setup to make it available.
  - That FAQ has a bad URL at present for the pkg-config download, but at the moment it was available at freedesktop.org.
  - Run ./configure from the directory where pkg-config is extracted.