The format of a Windows EXE file is proprietry to Microsoft so UNIX cannot execute that format - come to that, Windows cannot execute UNIX executables either (without an emulation layer).

Of course, if you are using Open Source then there should be no problem - just take the source code from the Windows machine and compile on UNIX - simples!

Of course it isn't that easy, but the principle is there - get a UNIX version of the executable and if there isn't one then build it yourself.