I was embarrassed in camera class when I couldn't turn off the flash so I started reading the manual again. I don't know much but here's what I think I know.
In Full Auto and the Basic Zones Modes (except Landscape&Sports) the camera flashes automatically, we have no choice except for the Flash Off Mode; the last icon on the dial (see manual pg. 47).
In the Creative Zone modes it never flashes unless we force it to by pressing the Flash Button on the front of the camera.
I'd love more (and/or corrected) information too.