Officially it should be used only for menus or sub-menus, from the ARIA spec 1.0:
Indicates that the element has a popup context menu or sub-level menu.
The Whatsock style guide covers this under the ‘modals’ section:
It might sound like a good idea to notify screen reader users that a ‘Popup’ is attached by adding the attribute aria-haspopup=”true” to the triggering element, but this is not a good idea.
… In short, don’t use aria-haspopup unless you are triggering a menu.
There is some discussion about expanding the meaning in future revisions, but for the moment assume it is for menus.
I gave an answer about Bootstrap’s tooltips which should help.
For pop-up browser windows, those are announced by screen readers anyway, no extra markup is needed. (NB: It helps to include a visual indicator of a new window for screen magnifier users.)