Qt is well-designed, well-documented, and cross-platform. It's been around for ages, and still under active development. Many Linux windowing systems are built ontop of Qt. It's very stable.
It's very nicely licensed, even for commercial projects. (LGPL = You can use it commercially, as long as you dynamically link to the DLLs instead of statically link).
On the flipside, it is HUGE. It has classes and functions for loads of stuff that you'll only need tiny pieces of every now and then, so it can seem quite overwhelming.
It also forces you to do things Qt's way, which can occasionally get annoying.
Further, it uses a signal-and-slot paradigm that, while very useful once you learn it, might throw you for a loop.
Qt even has it's own IDE, called QtCreator. It's really one of the best IDEs around for C++, even when not using Qt.
However, Qt is kind of finicky if not using QtCreator.
So, Qt is a big learning investment, but is not complex to learn. For a single small project, it's not worth the learning-investment. But if you're going to be making alot of desktop applications over the next few years, or if your project is a very big project, it's definitely worth it.
You can fully customize the appearance of your widgets, create your own widgets, or use any of the built-in widgets. It has a huge and active community, excellent documentation, and is extremely flexible. QtCreator has a built-in WYSIWYG drag-and-drop GUI builder (called QtDesigner) that's very nice to use, but you can also write your own code for classes (and you often use a mix of both anyway).
You can easily and rapidly assemble the visual interface of your project, so you can focus on the custom code that your project requires.
On the otherhand, if not careful, projects can rapidly become messy unless you actively make it a priority to keep your code clean.
I use Qt, and I love it alot, but it has its irritations as well.
It's so huge, I like to think of it as a collection of libraries (it's broken into about a dozen modules, but it could easily be subdivided further, it's so huge). It's similar to Boost in that manner: A huge collection of flexible and re-usable code sharing a common coding style and consistent interfaces, that encompasses many different purposes and features.