When I run mingw-get, it hangs for me at initialization, every single time. I tried both the pre-compiled version available at the download page, as well as building my own. For the record, I have Windows XP Home SP3.
Using gdb, I found the hang occurs at src/pkginet.cpp (pkgInternetAgent::pkgInternetAgent), when calling InternetAttemptConnect. The backtrace indicated that this constructor was called during DLL initialization (DLLMain), before even running the main() function. This seems to be due to pkgDownloadAgent being a static object of this class.
According to the MSDN page for DLLMain:
"The entry-point function should perform only simple initialization or termination tasks".
"Calling functions that require DLLs other than Kernel32.dll may result in problems that are difficult to diagnose"
"Because DLL notifications are serialized, entry-point functions should not attempt to communicate with other threads or processes. Deadlocks may occur as a result"
Anyway, moving the InternetAttemptConnect outside the constructor solved the issue for me.