Compilation error: "stddef.h: No such file or directory"

The error is because your gcc-core package and gcc-g++ are not of the same version. Either downgrade one of them to solve the problem or update both the libraries. Updating both the libraries is the recommended way.

I had this error on a fresh MinGW install, it had nothing to do with the installed packages mentioned in the current accepted answer by "Prasanth Karri". In my case the issue was caused by -nostdinc in my Makefile. I actually only needed that compiler flag when building for a different target platform (not when using MinGW) so I fixed the issue by removing that flag from MinGW builds.