MinGW, the Minimalist GNU for Windows, is the native port of GCC and Binutils that Qt uses for building their Windows version of the Qt tool-kit. Kai Koehne, an official Qt developer, re-sparked the Qt MinGW conversation this week about what package to officially support for the Qt 5.0 release. At the moment they're using MinGW 4.5 32-bit, but the latest MinGW release is now a port of GCC 4.7 except the problem with the official MinGW is that it's still 32-bit-only.
As possible alternatives, Kai tried out the 32/64-bit versions of TDM-GCC, Mingw-64, and Mingw-builds. TDM-GCC presented a nice installer but a somewhat stale GCC 4.6.1 + GDB 7.3.1 and not much activity all around, Mingw-64 is officially at GCC 4.5.4 but there's modern semi-official builds, and for mingw-builds they're closely following upstream GCC.
For why MinGW matters for Qt on Windows, "One might think that the only difference in these packages is the gcc version, but this isn't the truth. They also deviate e.g. in the COM headers, which can easily lead to build breakages ... That's why I think it's important to promote _one_ mingw 64 bit package as the officially supported one, and ideally even get it CI tested."
The mingw-builds project was able to build Qt 5.0 Beta out-of-the-box with only one minor patch being needed. What's being debated now is whether to add mingw-builds (based on GCC 4.7.1) to the list of tier-one configurations as a 64-bit version, support mingw-builds for 32-bit and 64-bit, or just leave it as-is without a more recent MinGW compiler and to be 32-bit-only.
This discussion is taking place on the project's development list. So far most feedback seems to be favoring Mingw-w64. Besides the MinGW-w64 fork supporting both 32-bit and 64-bit modes, it also includes updated files for supporting more recent parts of the Windows API.