This post will show you how to statically link libSDL.a into your application instead of dynamically link with SDL.dll

This post uses ffmpeg as an example, cross-compiled on linux with mingw32 compiler, which I think is a good complex example and useful example.

Prerequisite : Linux Debian or Ubuntu (or other Debian derived distributions, example mint)

Step 1 - Install gcc mingw cross-compiler

sudo apt-get install gcc-mingw-w64

This installs the cross-compiler

Step 2 - Download files needed

(1) Download SDL source code and the two cross-configure.sh and cross-make.sh scripts:

https://www.libsdl.org/release/SDL-1.2.15.tar.gz
http://www.libsdl.org/extras/win32/cross/cross-configure.sh
http://www.libsdl.org/extras/win32/cross/cross-make.sh

(2) Extract this to a folder in your home directory.

(3) Run this to cross-compile SDL 1.2.15 in a 32-bit library.
./cross-configure.sh
./cross-make.sh
sudo ./cross-make.sh install

(4) To then build the 64-bit library, edit cross-configure.sh and cross-make.sh by substituting i686 for x86_64 (only one place in each file) :
Change TARGET=i686-w64-mingw32
to
TARGET=x86_64-w64-mingw32

(5) Run this to cross-compile SDL 1.2.15 in a 64-bit library.
./cross-configure.sh
./cross-make.sh
sudo ./cross-make.sh install

Step 3 : Building ffmpeg

Download ffmpeg source code

git clone git://source.ffmpeg.org/ffmpeg.git ffmpeg.git

For 64-bit compilation :

export PKG_CONFIG_PATH="/usr/local/cross-tools/x86_64-w64-mingw32/lib/pkgconfig"
./configure --enable-memalign-hack --arch=x86_64 --target-os=mingw32 --cross-prefix=x86_64-w64-mingw32- --disable-shared --pkg-config=pkg-config --enable-gpl --enable-swscale
make

For 32-bit compilation :

export PKG_CONFIG_PATH="/usr/local/cross-tools/i686-w64-mingw32/lib/pkgconfig"
./configure --enable-memalign-hack --arch=i686 --target-os=mingw32 --cross-prefix=i686-w64-mingw32- --disable-shared --pkg-config=pkg-config --enable-gpl --enable-swscale
make

Optional : Statically link SDL

Edit config.mak for static linking of SDL
Note: This works very well for 64-bit compilation of ffplay. I don't know why I haven't been able for 32-bit.
Add the things in bold.
LIBS-ffplay=-mwindows -L/usr/local/cross-tools/x86_64-w64-mingw32/lib -lmingw32 -Wl,-Bstatic -lSDLmain -Wl,-Bstatic -lSDL -lwinmm -lgdi32 -ldxguid
(...)
EXTRALIBS=-lavicap32 -lpsapi -lole32 -lstrmiids -luuid -lws2_32 -mwindows -L/usr/local/cross-tools/x86_64-w64-mingw32/lib -lmingw32 -Wl,-Bstatic -lSDLmain -Wl,-Bstatic -lSDL -lm -lpsapi -ladvapi32 -lshell32 -lwinmm -lgdi32 -ldxguid