If there is text on the screen, and I have a cursor, I want to be able to select that text. It's okay if I can't cut it or delete it, but I should be able to copy it under almost every set of circumstances.
Examples where I want it: the text in BAlert boxes. Other non-editable text presented in dialogs. Static label text for widgets. Text for radio button options. Others?
Areas where this probably wouldn't apply: Title Bars, Menus, Buttons, Password boxes. Others?
Grey areas: list boxes, drop-down boxes. For these it would be desirable but in some cases the execution might not be straightforward.