How can I get a overview and manage the default applications for file types? Most OSs show a nice summary about which application will be used to open a certain file type. Android does not seem to have such a function.

How can I track and manage the default applications?
As you maybe already know, for each application that currently is a default application for something, say a PDF viewer, you can reset this default in the application settings (Settings -> Applications -> Manage applications -> Your app -> Clear defaults). After this, the next time you perform the action (e.g. open a PDF), a popup will appear, letting you choose a new default.

As far as I know, this is all you can do with stock Android.

There are however, 3rd party apps, that give you an overview of the currently set default applications for common things, e.g. Default App Manager.