These British mounted police do regular performances showing the incredible discipline and steadiness of their fabulous horses. Whether it's jumping through rings of fire or removing the entire saddle while riding a steady canter (wait for it at the end of the video!) these horses and riders are really impressive. Horses selected for police work have to deal with crowds, traffic, noise, gunfire and all sorts of scary things. Only the most steady and brave graduate from the training programs.
I saw a Mexico City mounted police display once, and they did some nifty acrobatics, such as four riders galloping in a group, swooping down on a fifth guy, with each rider grabbing either an arm or leg and carrying the man around like an airplane. I'll dig up some more police horse videos in the future. The level of trust these horses display is really something.
Update: Here is the official website of the Metropolitan Mounted Police (of London, UK), which has interesting info about how they select and train the horses.