In my experience, the word "over" is rarely used. Almost all ATC/Pilot transmissions imply "over" at the end of the transmission (meaning the person you are transmitting to recognizes that a reply [e.g. "over to you"] is being requested). Of course, if the pilot or controller is responding to a transmission and does not expect a response back, the word "over" would not be used.
If, as a pilot or controller, you make a transmission that implies that a response should be made, but a response is not made, the word "over" can be used in a subsequent/repeat transmission to emphasize you are awaiting a response.
As an example, in my opinion, if the pilot says "Bay approach, this is November 12345" and nothing else, the word "over" might be used at the end (e.g., "Bay approach November 12345, over") signifying that the transmission is over and a reply is expected. However, even without the word "over" being used it is likely that the pilot would receive a response from Bay Approach.
But, if the pilot says "Bay approach, November 12345, 15 miles south of Oakland inbound for landing with information Charlie," this makes it fairly clear that the transmission has ended and what type of response is expected from Bay approach control. In this case, adding the word "over" should not be necessary.