Building GDB on Windows
You can do this with either MinGW or Cygwin. You can also do it with MinGW in cygwin.
MinGW
I recommend doing this with https://www.msys2.org. Make sure to use the MinGW compiler, not the MSYS compiler.
pacboy -S gcc
You may also need misc. tools:
pacman -S dejagnu bison git make
With that setup, ./configure && make should just work.
I don't know how to make make check work, please update this page if you know.
MinGW on Cygwin
Use the cygwin installer to install the MinGW compilers. Then make sure that configure finds the right compilers. There's probably an easier way but I use: ./configure --build=i686-w64-mingw32 --host=x86_64-w64-mingw32
Cygwin directly
./configure should just work.