For ubuntu,

Configure -sstatic -prefix=/Qt_Static
make/ming32-make sub-src(it only build the source code)

cd to your application
PATH = link to Qt static Install folder
ming32 -make distclean
qmake -config release
make/ming32-make

After doing these process it will create a binary file i.e yourapp.bin(X11/linux) or yourapp.exe(Win32).

Dependency Walker is also one application for creating standalone application.