Last week there was a very sad occurrence at a popular Philly dog park - two dogs were playing when one dog's mouth got caught on the other's collar. The dogs panicked and the end result was that the collar suffocated it's wearer until he died. This is such a terrible story, and so sadly preventable. But the reality is that many people don't realize that their collar can make such a huge difference.
Those in the dog biz (especially doggy day cares, where off-leash play is a big part of their day) see jaws caught on collars as a somewhat regular occurrence, and they have rules that only allow easily removed collars such as velcro play-safe collar or break-away collars for life-saving purposes. Some dog folk prefer that dogs 'play naked' to completely prevent the risk of being caught up, but that should be decided based on the dog in question.
Martingale collars have become a very popular collar, although they originated for long-necked greyhounds and other sighthounds; they are a kinder variety of 'choke' collar and they need to be slid over the head to be removed. If a dog's jaw is caught under it there is no way to remove the collar aside from cutting it, and sharp implements are not always at hand.
Metal choke collars would also be very difficult to remove in this situation, as they are slipped off and on over the dog's head. These collars are often used incorrectly anyway, where they are always in 'choke' mode instead of loose when not engaged. I feel that these collars should only be used in a training setting, and by someone who knows how to use them.
Prong or Pinch collars are a training collar that will pinch the skin around the neck when pulled tightly. They are also typically used as slip over the head types, and although you can theoretically separate the collar at any of the joints it would be close to impossible with another dog's jaw pulling it taught. Many people have issues with these collars in general, as they can be considered cruel. I will not get into that discussion today, as any tool that is used properly may have it's uses; proper use is just not as common as I would like.
Buckle collars may not be removable in time to prevent this type of incident, and even snap collars might not be that helpful if the release is in the dog's mouth or unreachable during an incident.
There are so many nice collars out there - fun designs, fancy bling, tooled leather, personalized and what have you. And there is no reason that your dog can't have all of these in their wardrobe, to be used on walks (a sturdy, well-fitting collar is most appropriate for walks anyway). But when your dog is engaged in off-leash play, or in a crate, or even in your back yard, go with the safer option of a quick-release collar or none at all.