Basically it's up to you. Linux applications are common to be portable (unlike for Windows application). Although it's all about your will (do you want your software Windows-only, or portable).
It's possible to write easily portable software on Windows, and it's also possible to write non-portable software on Linux. For example we're sticking in all our applications to standard libraries (basically *just* bare standard of libc, (sometimes libstdc++ - depends on language we use)) and portable libraries (OpenGL, OpenAL, DevIL, GTK, ODE, etc.) - most of them are also open source by the way. E.g. we're basically trying to make our software system independent.
We're writing & testing all our software under both systems. So far we haven't met any system-specific problem!
#larspensjo - I object to port of D3D applications. If you rewrite your D3D functionality to WineD3D (this actually makes your software portable - and use OpenGL instead of D3D in the end), although I don't actually know how much work it is, because I haven't worked with WineD3D.