Tools Summary

I wanted to explain, briefly, what each tool in the dog training toolkit is used for.  I'm going to start with the tools I use and recommend, and then move on to the ones I don't.  However, I'm not going to start a debate, or vilify other trainers who do use them.

Tools I use and recommend:

1. Standard buckle or tag collar.  This collar is not intended to be for training or walking purposes.  It is purely decorative.  Walking a dog with leash attached to the tag collar can cause major tracheal damage should the dog lunge after something or pull for an extended period of time, and is not recommended.
2. Martingale collar.  The wider, the kinder.  This collar, when fitted properly, is inescapable.  So for dogs with an impressive display of flips, turns, and bucks to escape or back out of their normal gear, this is an excellent tool.  Contrary to what I've heard from some other trainers, martingale collars do not help with leash pulling.  They were designed for sighthounds, whose extremely narrow heads allow normal collars to come off, even without trying to slip them.  I use them in conjunction with front-clip harnesses, like the Balance Harness, as well as head collars, like the one by Dogs My Love.
3. Harness.  There are several types, and I wanted to describe the ones I don't recommend first.  There's step-in ones that buckle on the back -- which is great for head shy dogs.  However, I find the buckle digs into the spine if the dog pulls forward or lags behind.  Then there's types that have a strap that goes straight across the chest and shoulders, such as the Easy Walk, ComfortFlex, and Freedom harnesses.  These harnesses seriously impede movement and affect the natural gait of the dog.  There are harnesses designed for pulling sleds and weight pull sports, but aren't used for dogs on leashed walks.  There are various types of padded harnesses intended for maximum comfort on hikes -- which I do recommend.  My personal favorite is Ruffwear's Front-Range harness, which also has a tab in the front for leash attachment to inhibit mild pulling.  I highly recommend this harness in conjunction with my K9 Lunging Method for teaching leash walking, as well as freedom of movement for hiking or doing parkour.
4. Head collars.  This is a management tool only, to inhibit extreme pullers when there isn't time for training.  That, or the dog will be in an environment beyond their current level of training.  I don't prefer the ones with narrow bands, like Gentle Leader and Halti, due to the numerous scars left on dogs who pull on them for extended periods.  I like the one you can order on Amazon by Dogs My Love.  These are collars that are based on negative reinforcement, so there should NEVER be constant pressure on the device.  Give and take.

Now I wanted to get into the tools that I have used before, and don't recommend:

1. Slip or choke collar.  This collar, when used correctly, is based on negative reinforcement.  The tighter the collar becomes, the more aware the dog becomes, and so the dog yields to the pressure.  The looser the collar is, the more rewarding to the dog, so the dog learns not to pull.  However, it is very easy to misuse this collar, leading to tracheal damage, cutting off the airway, and in extreme cases, choking and suffocation until unconscious.
2. Prong or pinch collar.  This collar was designed to create even pressure points all around the neck, and avoids tracheal damage from slip, martingale, and buckle collars.  It looks like a medieval torture device, but isn't when used correctly.  I don't recommend using it to inhibit reactivity.  The fallout of doing it incorrectly is highly likely.  I have seen it used successfully on leash pulling and loss of focus.  However, it is very easy to over-correct, and leaving it on too long or having it poorly fitted can lead to collar sores.  The dogs become collar wise, and are no longer as well-trained when the prong collar is off.
3. Electronic (e), shock, or stim collar.  Sends various intensities of electric stimulation to the skin.  Also has beeping and vibration functions.  I've seen the vibration function used successfully with some deaf dogs.  I have seen plenty of seemingly comfortable dogs with e-collars.  However, I've seen the beeps make dogs paranoid about microwave timers, smoke alarms, and cell phone notifications.  I've seen dogs yelp from a stim turned up too high.  I've seen burn marks from a cheap shock collar.  I've seen dogs become wise to the collar, and fail to respond when not wearing it.  In desperation, I was convinced to try this collar on a dog of mine.  With proper guidance, I would say it did help where nothing else did as far as her ability to focus around high distractions.  However, it was not the cure-all that was promised.  I've since learned techniques that would allow me to never need it again on a physically healthy dog.  I do believe they may have their place for some deaf dogs.

In short, all tools are bandaids, and don't replace proper training.  Focus on doing the work, not on what tool is used.  Watch the behavior of the dog:  is the dog happy, eager to work with this person, and performing well?  Is the owner pleased with the dog's wellbeing and training?  Then I have no complaints.  However, I feel it is my duty to introduce methods and tools that are less aversive, and still accomplish the training goals for the dog efficiently and effectively.