It's possible to make statically linked applications but it's pretty much never done.

And it's against the linux packaging mantra, where you should be able to "apt-get install libqt" for example (noting that libqt package is completely detached from the release cycle of your application).

This leads to a ton of accidental dependencies and they're tied to the OS release. Even the simplest of apps might eventually depend on libc, pcre, openssl, etc...

Windows is simply different on this aspect. It's more friendly to static builds and the system libraries are more stable. If you built against some win32 API or the Visual Studio 2005 SDK, the DLL are still present and working.