Hi bobef,
Are you looking for GCC as a cross-compiler? That is, you want to make Linux binaries on a Windows box. It's possible, as I understand it (never done it myself) -- look for instructions on building GCC as a cross compiler.
Or are you looking to compile Linux source code on a Windows box as a Windows program? In which case I recommend Cygwin from the www.cygwin.com URL, which incorporates both MinGW (GCC making "pure Windows" programs), as well as a Cygwin (GCC making "Unix lookalike/workalike programs dependent on the Cygwin.dll layer").
Note: if you install Cygwin, by default, the installer only installs a minimal subset. Either make sure you grab all the GCC components (under the dev label), or just install everything at the top-most level (although that uses a lot of disk space and takes some time to install).
HTH, --Eljay