Consider, for instance, an e-mail client that for whatever reason requires obtaining a password. Should the dialog be part of an existing, probably sovereign posture, window? Or should it pop up? Equivalently, on a webapp, should it switch to a different page or use the current one.
As I see it, the disadvantages of pop-ups are that they are pop-ups(!) and breaks the association with the rest of the app.
The pop-up solutions seems the most popular solution. Even my VPN client I have to open a small dialog and then push a button to get the password prompt.
Examples of inline prompts are more limited. Some webapps, such as Twitter, slide open a dialog (even with http - grr). PuTTY prompts for SSH passwords in the terminal window, although here the motivation may be uniformity with telnet (where the protocol does not deal with passwords).