As far as I know and have understood in my experience with Qt, it's a very good and easy to learn library. It has a very well designed API and is cross-platform, and these are just two of the many features that make it attractive. I'm interested to know why more programmers don't use Qt. Is there a deficiency which speaks against it? Which feature makes other libraries better than Qt? Is the issue related to licensing?
I don't really intend this to be a bashing answer, but these are the reasons I do not personally use Qt. There are plenty of good things to say about it -- namely that the API works most of the time, and that it does seamlessly bridge platforms. But I do not use Qt, because:

In some cases, it just doesn't look like native programs look. Designing a single UI for all platforms inherently is not going to look right when moved from machine to machine, for various visual styling reasons. For example, on Mac machines, split bars are usually relatively thick, and buttons are small and rounded with icons. On Windows machines, split bars are typically narrow, and buttons are more textual, with more square designs. Just because you can write one UI for every platform does not mean that you should for most applications.
Qt is not just a link-able set of C++ libraries. The build system being used requires the translation of certain files into extra source files, which makes the build process much more complicated when compared with most other libraries.
As a result of (2), C++ IDEs and tools can flag Qt expressions as errors, because they do not understand Qt's specifics. This almost forces use of QtCreator or a textual only editor like vim.
Qt is a large amount of source, which must be present and preinstalled on any machine you use before compiling. This can make setting up a build environment much more tedious.
Parts are mostly licensed under the LGPL, which makes it difficult to use single-binary-deployment when one needs to release under a more restrictive or less restrictive license.
It produces extremely large compiled binaries when compared with similarly written "plain old native applications" (excepting of course applications written for KDE).

