There are two types of martingales; a standing and a running. Both of them prevent a horse's head from coming up. However, if it has to be used, it's just a training aid, it should not be used as a permanent fix, that's what training is for.
The standing martingale is attached at the girth to the noseband, like this;
The running martingale attaches at the girth and has two straps that come up, with a circle you run your reins through. Like this;
^^Nutty, here in the US, we keep it simple and I have only ever heard of the 2 that Ricci posted. To me, a running martingale is nothing more than a crutch for people with bad hands. IMHO, if a person can't get their horse's head down without the use of items like this, tie-downs, draw-reins, etc. then they need to work on themselves before they try to fix the horse.
A Combined martingale is a Standing and running combined into one piece - haven't seen one for years and I've never had to make one.
The Irish martingale is primarily used in racing - it's basically a short strap ( about 6" ) with a ring on each end that the reins go through, this helps to keep the reins from parting or flapping around too much which would be dangerous considering the activity, ever seen a horse go over The Chair at Aintree and you get the picture
A bib martingale is like a running martingale with a panel of leather joining the two ring straps together - so it's like a combined running martingale and Irish martingale , in the past primarily used for racing ( I've made about 50 for Newmarket ) but now I also see them in the showjumping circuit
The triangular panel is needed or there would be a gap which a horse could put it's leg through , which would be a disaster.
A Market Harborough is like a running martingale - except that the two ring straps are a lot longer and have a small clip on each end - these pass through the bit and onto a small 'd' fitted onto a pair of reins, they have a similar effect as a running martingale but are a lot stronger . They also have a similar effect to draw reins in bringing the head down but the downwards pressure is released when the horses head is in the correct position ( draw reins do not )
Although I would agree with you in that most of these are not needed in normal circumstances they are very useful as training aids and should be removed when not needed, some are however almost essential in competitions such as showjumping / cross country or racing , as the horse gets a lot of adrenaline in its system ( and most competition horses are either warmblood or hotblood ) and get rather out of hand and excitable.
I wouldn't call John Whittaker / Rodrigo Pessoa / Zara Phillips etc novice riders , they do use martingales for good reason - and I don't think they need to work on their riding .
I hope that clears up the martingale issue -
Nutty ^ you are absolutely right, maybe these other martingales are not used in the US, I don't know. As for people saying riders who use a martingale need to improve their riding, this is rubbish. I don't think it is a good idea to use them when schooling and when working quietly at home. If you are jumping at a show whether it is a speed competition or not if your horse is getting excited and throwing its head up it will completely ruin your round! You CANNOT school a horse not to get excited when jumping if they find it fun and some horses jumps are ruined because the rider wants them to be on the bit and cannot accept this particular horse jumps with a natural style of having its head up, however it is not possible to win competitions with your horse sticking its head up like a donkey. Riders without martingales who have horses like this often result to sawing with the reins which can damage to the mouth and forces the head down, not on the bit.
PS: I know I wasn't really answering the question, but didn't need to as Nutty has done it well already, just wanted to stick up for Nutty Saddler
As far as I'm concerned, they're really all just variations of the same thing, or maybe two things, lol. I get it though, it just breaks everything down a lot further. I'm not knocking down your knowledge, or arguing with it, it's always fun to learn something new. I'm just saying. =]
Oh, and it's also entirely possible to teach a showjumping or cross country horse how to carry itself with it's head lower and being more or less on the bit, even though it's excited. It's harder to do at a faster gait, so they won't maintain the same level of collection as a dressage horse, but they can do a successful jumping round without running around like a giraffe. It is still a lack of training.