I decided to put this page together since I get so many questions about different gear. There are lots of gimmicks and trick equipment out there. Many different pieces of horse gear is used in varied ways, some good and some bad. I will try and add new gear and give my opinion about it and it proper uses. If you come across something you want added, email me and let me know.
Bits: I personally am not a fan of bits. I am not a bit expert and there are many other sites about bits with a lot more information. Metal in the mouth is not horsemanship. It is a cheat, it is a shortcut, it is controlling a horse with pain and fear. Does it work? Yes. Lots of things works with horses, it does not make 'em right. All bits or control devices have the potential to hurt the horse. The reins and the hands of the people holding them make them bad or good. I will try and list some pros and cons under each image. There are basically two types of bits, Leverage and Non-Leverage (Direct pull).

The above bit is a standard curb also called a grazer bit. This bit is a leverage bit. The longer the shank, the more leverage it has. Leverage bits squeezes the bottom part of the jar between the torque of the shank and the curb strap/chin strap. Notice the term strap and not chain. A chain does not give, a chain hurts, chains and horses are NOT a good match.

The bit above is another version of curb bit, notice the longer shanks, more leverage, more pain with less pull.

The above image is a standard snaffle. Non-leverage bit. The reins attach to the bit ring and when a rider pulls, it give the same amount of pressure as the pull. Not so with leverage bits. Depending on the length of the shank will determine what the ratio is. Example is a three inch shank will have a 3 to 1 ratio, which means if I pull with 2 pounds of pressure the horse feels 6 pounds, if I pull with 5 the horse feels 15 pounds. Some bits are 5 to 1 or 8 to one, very bad. It is hard to be soft with you touch the reins and your horse feels an 8 pound pull. Not to mention if you accidentally pull with 10 pounds from fear or reaction, you horse's jaw feels 80 pounds of pressure. Lots of people think that just because a bit has a link or broken mouthpiece, that the bit is a snaffle and less painful, this is incorrect.

The above image is shows a pretty chain attached which goes under the horse's jaw. This is the pain device and this is where the horse feels all the pounds of pressure when the rider pulls on the reins.

The above image shows a Leather curb/chin strap. Leather gives, unlike chains, leather stretches and is much less painful than a chain. So even thou this bit has shanks and is a leverage bit, it is kinder and less painful than a longer shank bit or a chain chin strap. The device in the port is a brass ring that spins, also known as a cricket. This allows the horse to spin and play with the cricket, this also helps produce saliva, this helps lubricate the bit so it is not dry and rubs the corner of the mouth raw.

The above image is some different curb (leverage) bits. Notice "M", this is commonly called a Tom Thumb bit. Many think a Tom Thumb is a snaffle or softer bit since the mouth piece is linked (broken), this is very far from the truth. The Tom Thumb is one of the most aggressive and painful bits out there. See this article on the Tom Thumb bit.

The above image shows some different snaffle bits. All Non-leverage bits, direct pull, 1 for 1 ratio. Many people will put a chin strap on a snaffle, but is does not put pressure under the chin since their is no leverage and no shanks. A chin strap on a snaffle helps stop the bit from getting pulled through the horse's month, which normally would occur on the O ring snaffle (top), the egg butt, D ring and full cheek have more contact on the side of the mouth and face so they are less likely to get
pulled through a horse's mouth.
The image to the right shows a curb bit with a head stall attached. The number 15 is called a brow band, the number 2 adjust the piece that holds the bit so it adjusts how tight the bit is in the horse's mouth. The number 12 shows where the curb/chin strap would attach. The number 5 shows the throat latch, some head stalls do not have a throat latch, some people prefer it since it could stop a horse from rubbing off his head stall on a tree or post.

The image to the right is called a Mechanical Hackamore. This is called a Bitless bridle since the it has no mouth piece (nothing in the mouth). However, notice the long shanks, this makes this a leverage bit. When the rider pulls on these reins the torque and pressure is on the horse's top of the nose and bottom of the jaw. Cool, double the pressure and pain from one pull. :( This can be better than metal in the mouth, but can be very painful since it is a leverage bit, so every pull is compounded and enhanced. 
The image to right is called a traditional Hackamore. the piece around the nose is called a bosal. The hanger is the head stall that holds the bosal. The rope under the chin is called a Fiador, it holds the bosal in the proper position and prevents it from being pulled forward and over the chin. The reins are called Mecate and are normally about 22 feet long. All of these pieces together make this a hackamore. This is another form of a bitless bridle, no metal in the mouth. However this is a Non-leverage bit, a direct pull bit, so it has a 1 to 1 ratio, one pound of pull gives one pound of pull. This is my favorite style of bit. No leverage, no metal in mouth and takes finesse to use properly. You can be soft and communication is still clear.
The photo to left is the actual tie down strap, it will hook to the front cinch on one end and to a halter or nose band. The image to right is a leather nose band that fits around the horse's nose. Tie downs are bad in my opinion. They are a cheat and teach a
horse to pull and be stiff necked. Many will tell you
teaches a horse to keep his head down, it ain't so. It forces a head down, it does not allow a horse to raise his head, but it teaches a horse to pull and be stiff. When I see a horse with a tie down it only confirms that the rider has hard hands, does not understand horses and does not understand what a tie down does. The really bad thing about this is if you forget your horse has this on and your horse gets in water he will drown, since he cannot hold his head up due to the tie down. Just another case where a horse pays for people's ignorance.
Breast Collar:
There are different types of breast collars. Most all help keep the saddle in place and minimize movement of the saddle. Some are low and go across the shoulders like the image on the left. While others go up higher and are known as pulling harness type of collar, like the image on the right. I prefer the pulling harness since it tends to stay out of the way of the movement of the shoulder.
Saddle Parts:
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In the image above the flank billet holds the rear cinch and the Flank cinch is the same as the rear cinch. The hobble strap is also known as the stirrup hobble. The rigging is where the front and rear cinch connects to the saddle. The latigo is the leather piece that tightens the front cinch. Below is the parts of an English saddle.
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Lariat:
The image below shows a lariat tied to a saddle, also known as a lasso. This is an invaluable piece of equipment. It comes in handy for 101 uses and I will not be caught riding without one. It can be a lead rope, a sack out tool, can pony a horse, catch an injured critter, drag something, hang something, be a picket line, it doubles as quick grab for a bucking strap or nightlatch and many other uses.
Martingale or Training Forks:
The picture to the left is also called German or Running Martingale. Some call these training forks. The idea is to help the horse feel pressure when he puts his head too high and to help the horse feel a little more downward pressure when the rein is pulled. These are commonly adjusted way too short and put too much pressure and lose their training benefit. It is not a tie down and is not to keep or force the head down, unfortunately, that is what many use them for.
Training Harness:

A training harness also known as a cirsingle or driving harness. It is a basic cinch with a top part to encircle the horse's girth. It enables you to connect reins to and put them through the harness and drive the horse from behind. It can also be useful when getting a horse to lay down. You can do the same thing with a saddle, but this is less bulky not as many parts to get in the way of your training.
Side Pull:
A side pull is another form of bitless bridle. It is a non-leverage device. Putting reins on a rope halter is another from of a side pull. The
image to the left is an English style of side pull and the image on the right is a western style of side pull. There is another English model that makes a "X" under the chin so it puts different pressure points when you use the reins, but it is still an non-leverage type device. If you can ride in a halter, you can ride in a side pull, if you can ride in a side pull you can ride in a bosal or hackamore.
Here is another type of side pull where the reins cross under the chin. In the photo to the right you can how pulling on the right rein will put pressure on the left side of the face and will cause the horse to move right, away from pressure.
Hobbles:
I have a page that describes this in detail. Hobble Page
Whip or Crop:
This is the most misused training tool out there. It is used way too often to hit the horse, to beat the horse, to scare the horse and none of that ever teaches a horse. I use whips to sack out a horse and to desensitize them to the sound and fast movement. I do not use it to lounge or scare the horse.
Chaps and Chinks:
This is another piece of needed equipment. If you spend much time on a horse you would wear these. They keep you warm, they help keep flies away, they protect against scrapes and bangs and they help keep you in the saddle. Lots of benefits to chaps. The main different between chaps and chinks are chaps go all the way over your boot and chinks only go past your knees.
Sho Fly:
You will see these hanging off different areas of a saddle or headstall. As they swing the help keep the flies off your horse. So by putting one or two on your cinch, it swings and helps your horse.
Blinder or Blinkers:
These are used to take away a horse's ability to use their vision. People think that if a horse can't see something then it won't be scared. That should sound silly to just about everybody. If you close your eyes I can scare you more than if your eyes are open. I am not a fan of anything that takes away horse's natural ability to use their senses.
Horse Blankets:
I have to try really hard not to get on my soap box on this. A
horse does not need a blanket most of the time. The short list of problems with blankets are they are too hot, they make noise, if they get wet they are worse, they get caught up on things, the buckles cut horses, they prevent the horse from growing natural protection, when left on they make the horse sweat and increase the chance of a horse getting a chill or sick and the list could go much bigger but you should get the point.
Slobber Straps: 
These are pieces of leather that fold over a bit ring (normally a snaffle bit). Then the reins are connected to these pieces of leather.
After I started this page I found this great link that explains just about everything. So this check it out if gear is not listed here.