Please don't hesitate to expand this answer.
Tkinter is the toolkit that comes with python. That means you already have everything you need to write a GUI. What that also means is that if you choose to distribute your program, most likely everyone else already has what they need to run your program.
Tkinter is mature and stable, and is (at least arguably) quite easy to use.I found it easier to use than wxPython, but obviously that's somewhat subjective.
Tkinter gets a bad rap for looking ugly and out of date. While it's true that it's easy to create ugly GUIs with Tkinter, it's also pretty easy to create nice looking GUIs. Tkinter doesn't hold your hand, but it doesn't much get in the way, either. Tkinter looks best on the Mac and Windows since it uses native widgets there, but it looks OK on linux, too.
The other point about the look of Tkinter is that, for the most part, look isn't as important as people make it out to be. Most applications written with toolkits such as Tkinter, wxPython, PyQT, etc are special-purpose applications. For the types of applications these toolkits are used for, usability trumps looks. If the look of the application is important, it's easy enough to polish up a Tkinter application.
Tkinter has some features that other toolkits don't come close to matching. Variable traces, named fonts, geometry (layout) managers, and the way Tkinter processes events are still the standard to which other toolkits should be judged.
On the downside, Tkinter is a wrapper around a Tcl interpreter that runs inside python. This is mostly invisible to anyone developing with Tkinter, but it sometimes results in error messages that expose this architecture. You'll get an error complaining about a widget with a name like ".1245485.67345" which will make almost no sense to anyone unless you're also familiar with how Tcl/tk works.
Another downside is that Tkinter doesn't have as many pre-built widgets as wxPython. The hierarchical tree widget in Tkinter is a little weak, for example, and there's no built-in table widget. On the other hand, Tkinter's canvas and text widgets are extremely powerful and easy to use. For most types of applications you will write, however, you'll have everything you need. Just don't expect to replicate Microsoft Word or Photoshop with Tkinter.
I don't know what the license is for Tkinter, I assume the same as for python as a whole. Tcl/tk has a BSD-style license.
It's build on top of Qt, a C++ framework. It's quite advanced and has some good tools like the Qt Designer to design your applications. You should be aware though, that it doesn't feel like Python 100%, but close to it. The documentation is excellent
This framework is really good. It's being actively developed by Trolltech, who is owned by Nokia. The bindings for Python are developed by Riverbank.
PyQt is available under the GPL license or a commercial one. The price of a riverbank PyQt license is about 400 euro per developer.
Qt is not only a GUI-framework but has a lot of other classes too, one can create an application by just using Qt classes. (Like SQL, networking, scripting, …)
Qt used to emulate GUI elements on every platform but now uses native styles of the platforms (although not native GUI toolkits): see the documentation for Mac OS X and the windows XP style
Packaging is as simple as running py2exe or pyInstaller. The content of my PyQt app looks like this on windows (I have used InnoSetup on top of it for proper installation):
pyticroque.exe PyQt4.QtGui.pyd unicodedata.pyd
MSVCP71.dll PyQt4._qt.pyd unins000.dat
MSVCR71.dll python25.dll unins000.exe
PyQt4.QtCore.pyd sip.pyd _socket.pyd
QT comes with a widget designer and even in recent versions with an IDE to help design Qt software.
PySide is a LGPL binding to Qt. It's developed by nokia as a replacement for the GPL PyQt.
Although based on a different
technology than the existing
GPL-licensed PyQt bindings, PySide
will initially aim to be
API-compatible with them. In addition
to the PyQt-compatible API, a more
Pythonic API will be provided in the
future.
wxPython is a binding for Python using the wxWidgets-Framework. This framework is under the LGPL licence and is developed by the open source community.
What I'm really missing is a good tool to design the interface, they have about 3 but none of them is usable.
One thing I should mention is that I found a bug in the tab-view despite the fact that I didn't use anything advanced. (Only on Mac OS X) I think wxWidgets isn't as polished as Qt.
wxPython is really only about the GUI-classes, there isn't much else.
wxWidgets uses native GUI elements.
An advantage wxPython has over Tkinter is that wxPython has a much larger library of widgets from which to choose from.
Others
I haven't got any experience with other GUI frameworks, maybe someone else has.
