There are three types of brakes used. The first as mentioned are pneumatic brakes. (air brakes) They have calipers lined with bronze for brake pads, bronze being an alloy of copper, tin and sometimes other soft metals. The knife blades mounted on the trains are harder metals such as steel. They are located on the bottom or sides on most roller coasters. Inverted are usually mounted on the track, with the excpetion of Arrow Dynamic's early suspended coasters which had the brakes under the cars. The basics of operation is compressed air forces a cylinder or air bag to either open or close the calipers and a spring or another cyliner return it back to position. The brake pads put pressure onto the knife blades slowing the train down. Usually a system lowers the pressure to make braking smoother. When conditions permit, the brakes open and allow the train to proceed. A system fault or Emergency Stop will override the control system and force the brakes closed.
Secondly, a new concept with braking that has taken off are eddy current brakes. These are better know as magnetic brakes. These brakes consist of brake calipers lined with rare earth magnets. (neodymium iron boron) The knife blades are copper alloy which has diamagnetic properties. When the knife blade passes through the calipers magnetic field, the copper reacts producing it's own magntic field that in turn opposes the calipers field. Since is doesn't rely on friction, the knife blades and calipers don't need to make contact This braking action relys on the knife blades movement through the field. Also the braking power is directly proportional to the speed that the blade passes the field. In other words: very low speed results in very little braking, high speed results in powerfull braking. In the end, eddy brakes can slow trains but are unable to hold a train in place. This is actually used to improve the reliability of the braking system. Since they can't hold a train, the brakes can be placed on a downward slope. This will allow the train to roll slowly through the brakes even when they are engauged. Because of that the brakes can be mounted permanently in the on position. This allows the train to slow down from high speeds to reasonable speed in a fail safe manner because of the lack of moving parts. After that more permanent brakes can be placed with drive tires to move the train through or brakes the can be turned off after the train slows down can be used. The calipers are mounted on the track blades are mounted on the trains for most roller coasters. Rocket coasters reverse this mounting for application reasons. Eddy brakes are used in conjunction with pneumatic brake or the next type of brakes.
The third type of brake are hidden in drive tires. Drive tires have three basic componets to move trains. It has an electric motor, a gearbox, and the tire. When you turn the motor off the train would contine forward. To prevent that from happening they put a parking brake with is little more than a pin that engauges a hole in the motor shaft. Usually these have connection to the motor windings so they only engauge when the motor is off. In most cases, the motors slow down before the train reaches the stopping position. This allows for better parking accuracy and less wear on the parking brake.
Goliath, eddy brakes. All of this rides brakes are permanetly mounted for added safety. You can see it takes a lot of drive tires to push the train through.
Top Thrill Dragster, eddy brakes in reverse position. These brakes lower before the train is launched, after the train passes each peice of track the brakes pop up because of the springs in the cylinders. After the train passes the launch completly, air is fed into the cylinders forcing them up for redundancy. During a rollback the train slows down over 3/4 of the brakes and rolls from there at a few feet per minute. To save time, the brakes can be lowered from the control panel for short periods of time.
Xcelerator, an aggresive slope rocket coaster. Note that some a permanently placed while others towards the end are the same as the ones on TTD's launch.
X, this ride uses Magnetic braking too.