There are five major types of bungee jumping. Everyone knows the first type of bungee jumping. This is the plain old bungee jump (if there ever was such a thing). Based on the natives from Pentecost Island in the South Pacific, this is where you jump off from a platform or other tall object. Attached either through a let harness or body harness to a bungee cord or cords, you propel toward the earth. Once the cord(s) reach their maximum elasticity, you would rebound a few times. Typical jumpers experience about 2 to 4 rebounds, giving them the feeling of weightlessness.
The second type of bungee jumping is called 'the catapult', 'reverse bungee', or 'bungee rocket'. In this version of the bungee jump, you start on the ground and propel upwards. You are actually attached to the ground using a variety of methods. Once the bungee cord is stretched and ready, you are released. This has the effect of shooting the jumper upwards into the air. There is some danger in this method of jumping however. The bungee cord has a tendancy to pull the jumper towards the object it is anchored to. In the case of the 'catapult' jump, it is usually a lift crane. The danger is that you could hit the crane on the initial pull upwards. Of course, after the initial rocket upwards, the jump is much like the normal bungee jump.
The third type of bungee jumping is called the 'twin towers'. This type of bungee jump has solved the collision issue created with the 'catapult'. In this version of the bungee jump, there are two towers or cranes with bungee cords attached to the jumper. These are set some distance apart, with the jumper in the middle. This has the effect of shooting the jumper straight up, since they are pulling simultaneously. This eliminates the issue for potentially hitting the platform or crane. Some commercial outfits use a metal cage with this type of operation. However, this does require a bit more calculations, as the added weight of the cage will increase the need for more bungee cords.
The fourth type of bungee jumping is called the 'bungee run'. However, as the name implies, it really doesn't involve any jumping at all. This type of bungee activity usually takes place down an inflatable runway. The object is for the runner to get as far as possible before the bungee cord pulls them back toward the anchor point. Competitions are actually held in this variation of the bungee sport.
The fifth type of bungee jumping is called the 'bungee trampoline'. This variation involves the use of a trampoline, in conjunction with poles and bungee cords. The jumper starts jumping on the trampoline, in a body harness, attached to bungee cords. The cords are attached to poles on the sides of the trampoline. As the jumper gets up higher and higher, the cords are tightened. Using this method, the jumper is able to go higher than they normally would with just the trampoline alone.
As you can see there are many types of bungee jumping in the modern bungee jumping movement. These are but a few of the more well-known examples. The future is sure to bring about even more variations of this extreme sport.