As far as I have seen, Tkinter is great for simple applications, teaching, or for when you don't need the features of a more comprehensive package like Qt or wxWidgets. These libraries can run several megabytes, and you may not need that. It's part of the standard library, so it's suited for this purpose. However, if you need more features, then Tkinter may not be the best choice.
Tkinter also used to look really ugly because it drew its own widgets on each platform; however, I think the version included with Python 2.7 uses native widgets now.
I don't think there are any specific applications; it's a general purpose library.