I signal left turns with my left arm, right turns with my right arm, for the reasons mentioned above. I don't usually bother with signalling stops, as I generally want to have both hands on the bars at that time.
One thing that I find just as useful as signalling my turns is using "instructional" gestures on motorists who seem confused or indecisive about what to do around me. For example, I'll sometimes gesture with the "come" gesture if they have the right-of-way and seem reluctant to claim it (as a way of acknowledging that I see them and plan to yield). Other times, where it looks like they might be thinking of failing to yield to me properly, I'll give the opening palm "wait" gesture in order to ask them to wait. That one is often useful for motorists who are turning onto the street I'm on from a side street or driveway, and who seem to be having trouble estimating my speed (you learn to read the situation after awhile). Since I've started doing these "extra" gestures, I've found I experience a lot fewer close calls and unnerving situations. A lot of motorists are genuinely just confused and inexperienced at driving around cyclists, and I see it as just helping them out by giving them some guidance. I generally give a friendly wave after they obey, too, in order to show good will.