Initial success or total failure.
Bomb Disposal generally falls under two categories, civilian and military.
Military bomb disposal units tend to deal with much larger explosives. These are weapons that have been fired and or dropped on something, and due to some flaw in the manufacturing process, did not explode when they were supposed to. While they generally could be safely left there unmolested, they do have a tendency to go off if disturbed. Thus, it's much safer to take care of the explosive, after getting everyone out of the blast radius. Most of their work is done either in places that have been bombed in the past, such as the millions of unexploded ordinances left, dropped on Laos by the United States Air Force during the Vietnam War. Another very important task of military Bomb Disposal personnel is the clearing of land mines, or depth charges.
Civilian bomb disposal, on the other hand, tends to deal with much smaller bombs, that happen to be placed in much more strategic positions.
These are the guys who deal with a package left on the steps of the provincial legislature. What's in it? 20 kilograms of C-4 on a timer? Maybe something rigged to go off when you move it. Or perhaps someone's committee report. Chances are that it's not actually an explosive, but considering the consequences, it's better to be safe than sorry.
So how do they do this? C'mon, you've seen it in the movies. You've gotta cut the red wire. Or is it the blue? Oh wait, yell... *BOOOOM*
Wrong. There shall be no cutting of wires. Bomb disposal is done from as far away as possible.
What people do to deal with bombs greatly depends on where it is. If it's laying in a field in the middle of nowhere, you're a lot more likely to just blow it up than if it's sitting next to a support column for a skyscraper. In all instances, the first thing done is evacuating the area.
The most useful tool of the bomb disposal expert is the robot. There are a lot of types of bomb disposal robots, but a lot of them have common characteristics. Most of them are tread mounted, and they will all have some sort of a camera mounted upon it, so that the operator can see what the heck he or she is doing. It'll have some form of arm to manipulate the bomb with, or its surroundings, such as opening a car door. They are mostly controlled via an umbilical cord stretching from the robot to the operator. The cord carries commands, relays data, power for the robot, and in some cases high pressure air, for pneumatic pistons and the like.
The higher end models will come with a variety of sensors to enable the user to determine exactly what type of explosive they're dealing with, if it is an explosive at all. These sensors can determine if you're dealing with a regular explosive, a nuclear ordinance, a biological weapon, or what have you. There's also x-rays which can let you see the inner workings of the bomb, which can definitely make things a lot easier.
Sometimes the nature of the bomb will allow it to be removed from the area. This, quite frankly, doesn't happen often. Most of the time these things are rigged so that once armed, if they're moved, they'll go off. However, you can determine that it can safely be moved, they've got these containment vessels, which will help prevent damage should the explosive go off while in transit. It'll then generally be moved to a safe location, and then detonated.
In most cases, a bomb will have to be taken care of on site, including almost every military bomb disposal. If a bomb is not home-made, some of the time you will be able to identify who manufactured it, and more importantly, the steps required to disarm it. Oftentimes, this will involve using another explosive to disable the firing mechanism of that explosive. Other ways of dealing with it include drilling a hole in the case, and setting the explosive on fire, in such a way that instead of detonating, it deflagrates, which will not cause nearly as much damage.
In the rare cases in which it is necessary for bomb disposal experts to personally work on a bomb, they have developed body armor to provide some protection. Featuring a great deal of padding on the chest, arms, legs, groin, and a rather sturdy helmet to protect the head. This will allow people to get much closer to a bomb, with less risk of injury if it does go off. And I say less, because there is no way to be totally safe. Especially on the one area that cannot be protected much without inhibiting the effectiveness of the bomb disposal expert, the hands. But, these suits are designed to protect against fragments travelling at supersonic velocities, so while they may not protect someone from injury, they're a hell of a lot more likely to save a life.
Update: I've been told about a new system called Zeus-HLONS, which uses a laser to do the same thing as mentioned above, drilling a hole in the casing and burning the explosive. The advantage of course, is that you are not required to get in close at all. This is a new technology, which is just being introduced by the United States Army. Sounds like a very cool concept, assuming that said bombs are not anywhere near stuff that you don't want blown up.
Bomb disposal had its start during World War II, when Great Britain was getting hit by German bombs from across the channel. Those guys would have to get in close, and do exactly what I told you up above not to do. Since then it has branched out to other areas, dealing with stuff like depth charges (Bomb disposal underwater will be just that much more dangerous), land mines, and homemade bombs used by terrorists of all sorts.
As technology to disarm bombs progresses, so does the technology to make them. For example, the IRA has taken to using cell phones to trigger bombs. Wait for the best moment, dial the number, and boom. In all, bomb disposal is an extremely dangerous occupation, only to be undertaken by those with nerves of steel.
As a side note, those robots are fun to play with. Driving towards people and snapping the claw menacingly is awesome.
SPG Media Limited, "Man-Portable Robots for EOD, Reconnaissance, Communications," Army Technology - Foster-Miller. 2004. <www.army-technology.com/contractors/civil/foster_miller> (December 28, 2004).
First Defence International Group. E.O.D. Bomb Disposal. November 25, 2003. <www.firstdefense.com/html/bomb_disposal_Equipment_Military_Police_LawEnforcement_EOD.htm> (December 28, 2004).
United States Navy, Explosive Ordnance Disposal Mobile Unit TWO. July 20, 2004. <www.cnsl.spear.navy.mil/eodmu2/mu2index.htm> (December 28, 2004).
Wikipedia, "Bomb disposal," Wikipedia, the free encylopedia. December 23, 2004. <en.wikipedia.org/wiki/Bomb_disposal>