As a driver in one of the most aggressive and dangerous areas of the United States, I've never felt worried when driving in and around LA. I'm sure to someone in LA, LA drivers are aggressive and dangerous but I think they pale in comparison to what I experience here. In DFW, people are ridiculously impatient. In LA, I've found that's not really the case since traffic is expected everywhere. I've had an easier time getting let into lanes, not cut off, and not tailgated in LA way more than here in DFW. Just my little anecdote for the thread.
Agree with the others who've said that just be aware of your surroundings, leave valuables either out of sight or take them with you, don't drive aggressively, and don't answer back any honks or gestures and you'll be fine.