I am really surprised by many of the answers in response to this question. Mainly I'm surprised because Yahoo Answers is all about knowledgeable people sharing their knowledge and experience (at least it should be), but I really see a lack of both in this thread.
What this Collar Is -
This type of collar is called a prong collar, and sometimes it's also called a pinch collar.
It is probably one of the most misunderstood training tools on the planet, both by dog owners as well as by some dog trainers. Some trainers advocate their use. Some think they are necessary. Others are completely against them. What it comes down to is who is using them, why, and how.
I see a lot of people who use these to control a difficult dog but who don't know how to use the collar correctly. They just heard or were told by a friend, family member, or trainer, that these collars can stop a dog from pulling. But they never go and see a trainer to teach them how to use the tool. They are the kind of people who slip the collar over the dog's head instead of disconnecting the links, and who don't know how to size it correctly. In the hands of those people, such a collar can be dangerous and do more damage than good.
However, any tool that is used by someone who doesn't know how to use it can be dangerous and damaging. Standard collars like the slip or choke chain are no different. Even modern "humane" devices such as head collars are no different. Even a flat collar can be dangerous.
First, let's get this out of the way: the prong collar is a training device. As a result, it should ONLY ever be on the dog when you are doing training: at class, on walks, or wherever else you train. This collar is not a 24-7 collar. It should not be left on the dog when you're not there holding the other end of the leash. It most definitely should never be used to tie a dog out or secure a dog inside a vehicle.
How to use this Collar -
A prong collar is fitted by removing links from the chain and fitting it around the upper part of the dog's neck. The actual "prongs" are not spikes, but rounded ends. As such, they don't pierce or prick the skin, they pinch it. (This is why this type of collar is also called a "pinch" collar.)
A prong collar does not give continuous or nagging corrections like most flat collars, choke chains and harnesses are. A lot of people let their dogs pull on flat collars or chokes. A dog cannot pull on a prong collar - the dog corrects itself for pulling. Pull = correction.
In all other circumstances, a correction is given by giving a short, quick tug on the leash and then immediately releasing the leash pressure again. This mimics the way an alpha dog corrects its subordinates by biting them on the neck - a quick bite for correction and letting go. This is something that dogs understand because it's in their nature to correct each other like this.
Because of the way the prong collar is used (when it is used correctly), it's actually a more humane and less damaging tool than other training collars on the market.
Collars can Cause damage!
Take the choke chain. Many people who have a problem with a prong collar will use chokes. A choke is much more difficult to use for an inexperienced person because it requires frequent adjustment to keep it behind a dog's ears. (Around the lower part of the neck - which is the strongest part of the dog - it is ineffective and useless!) A choke chain can also cause serious damage to a dog's neck and trachea, including cumulative damage with years of use. Collapsed tracheas and bruising are fairly common in dogs walked on chokes.
Take the head collars as well - Haltis and Gentle Leaders. Suzanne Clothier, the author of "Bones Would Rain from the Sky", has a very good article about the misuses and problems with head halters on her website, here - http://www.flyingdogpress.com/headhalters.html She also has an article on training with prong collars in the same area that is interesting.
A head halter is much more dangerous than a prong in the hands of someone who doesn't know what they're doing. I don't know how many times I've seen someone with a dog on a head halter *AND* a Flexi lead, letting the dog drift ahead at will, then yanking its head back.
Why People Don't Like Prongs
I think the problem people have with prong collars are that they assume they are painful and that the dog only behaves out of fear because of how the collar LOOKS. Both of those assumptions are wrong. The only thing such assumptions prove are that the person has not done any research about all training tools available and how they are used.
First, the prong is not a horrible painful device. As I've already explained, the tips of the individual prongs are actually rounded. When I explain to people about the prong, I have them slip it around their forearm, then give a quick correction. Most are surprised that it's not nearly as painful as they imagine. Add to this the fact that dogs have thicker skin than humans *and* fur on top of that, and it's not that harsh of a correction. It's a correction - yes - that's the whole point of using it, but it's not harsh or inhumane.
Second, the prong collar (or use of corrections in general) does not rule out positive training. Even positive training has room for corrections - once the dog knows a command and chooses not to follow it. There are many different types and kinds of corrections, and which ones you use depends on your dog's needs. Some dogs need stronger corrections while others are fine with a verbal correction.
Who uses this thing, anyway?
Consider this. Our law enforcement and military both use positive reinforcement for training their drug and explosives search dogs, and even their protection dogs. Dogs are rewarded for jobs well done - with tugs, kongs, or carrying off the bite sleeve after getting a good bite. These dogs are highly motivated, high drive working dogs. They love what they do. Yet the majority of agencies use either prong collars or choke chains on their dog. It's because they afford the handlers more control over a strong, drivey dog. Not because they're punishing and make the dogs fear their handlers.
If you're a pet dog owner and have a difficult dog - such as a large breed that can easily drag you down the road or a very drivey dog that will take off after any moving creature - I would much rather see you with a prong so you're in control of your dog, than with a choke or halti that can injure your dog (and you!) seriously when he/she decides to take off after a squirrel.
But I have to stress - ANY tool is only as good as who is using it. Learn how to use it correctly (have a trainer show you) and practice with it.
Lastly, I want to add that the prong collar is not currently illegal anywhere, including the UK. For some reason people keep saying that these collars are illegal in the UK or Australia in particular. That is not true. However, some countries restrict the import and sale of the collars to make sure they only are used by people who know how. (Which is pretty smart considering the amount of people I see who are completely clueless about using them.)