When I ride through parts of town with chaotic car and pedestrian traffic, I find that I need to limit my speed in order for my reaction time to be adequate. I told this to another cyclist one time and he laughed: "But the speed limit is 20mph here! You can do 20 and still be fine." But I don't believe that's accurate. Maybe a car can do 20 and be fine, but their braking system works differently. A driver is unlikely to flip their vehicle over if they brake suddenly at 20mph, but a cyclist is quite likely to either go over the handlebars or be unable to come to a complete stop quickly enough.
Some hold the theory that instead of braking, the urban cyclist should be quick to accelerate so that they can go around swerving cars and leaping pedestrians. But that isn't always possible. Earlier this week during the holiday shopping rush, I found myself in a situation where I was basically trapped between several moving objects simultaneously and had no choice but to slam the brakes: Two car doors in a row swung open ahead to my right while, at the exact same time, a pedestrian jumped into my line of travel (which was out of the door zone). I could not swerve right because of the car doors, I could not swerve left because of the moving cars in the travel lane, and I could not continue straight because of the pedestrian. Within milliseconds, I had to come to a complete stop.
Over time I have determined that my self-imposed "speed limit" when cycling through areas where such situations are possible needs to be 12mph at most. Any faster than that, and I cannot guarantee that I can come to an immediate stop safely. Do you have an urban speed limit?