There are thousands....Some of them are....
China (styles ・ list ・ wrestling)
"External":
Shaolin Kung Fu
Northern: Changquan ・ Fanziquan ・ Northern Praying Mantis
Southern: Bājíquán ・ Hung Ga ・ Southern Praying Mantis ・ Wing Chun
"Internal" / Wudangquan:
Baguazhang ・ Liuhebafa ・ T'ai chi ch'uan ・ Xingyiquan
Japan and Ryūkyū (Okinawa)
traditional: swordsmanship (kenjutsu) (Battōjutsu) ・ stick fighting (bojutsu) (Jōdō) ・ archery (kyujutsu) ・ spear (sojutsu) ・ unarmed (jujutsu) ・ Sumo ・ Kobudō ・ Ninjutsu
modern: Aikido ・ Iaido ・ Judo ・ Jūkendō ・ Karate ・ Kendo ・ Nippon Kempo
Korea:
Hapkido ・ Subak ・ Taekkyeon ・ Taekwondo ・ Tang Soo Do ・ Ssireum
Indonesia: Pencak Silat
Burma : Lethwei
Laos : Muay Lao
Malaysia: Tomoi ・ Silat Melayu
Thailand: Muay Boran ・ Krabi krabong ・ Silat Pattani
Philippines: Eskrima ・ Kuntao ・ Panantukan ・ Sikaran
Vietnam: Vovinam
Indian subcontinent
Bangladesh: Boli Khela, Lathi Khela
North India: Gatka (Sikh) ・ Inbuan (Mizoram) ・ Lathi (stick fighting) ・ Malla-yuddha ・ Musti yuddha ・ Malakhra ・ Mukna (Manipur) ・ Pehlwani (Persian wrestling) ・ Thang-Ta (Manipur)
South India: Kalaripayattu ・ Kuttu varisai ・ Marma Ati ・ Silambam
Pakistan: Malakhra
Sri Lanka: Angampora
Middle East and Central Asia
Greater Iran
Varzesh-e Pahlavani, Pehlwani
Folk wrestling: Armenian, Azeri, Mongolian, Turkish, Tatar, Uzbek,
Israel Abir-qesheth Israel
European
Historical fencing: German ・ French school of fencing ・ Italian ・ Spanish
stick fighting: Bataireacht ・ Baton fran?ais ・ Juego del Palo ・ Jogo do Pau ・ quarterstaff ・ singlestick
striking: Pankration ・ Greek boxing, Russian fist fighting
folk wrestling: Breton ・ English: Cumbrian, Devon, Lancashire ・ Greek ・ Icelandic ・ Scottish ・ Serbian ・ Swiss
Other
Africa: Dambe, Istunka, Canarian wrestling, Senegalese wrestling
Oceania: Mau rākau
Modern or hybrid
Olympic flag.svg Olympics: Fencing ・ Boxing ・ Judo ・ Taekwondo ・ Wrestling
Australia: Zen Do Kai
Bangladesh: Butthan
Brazil: Brazilian Jiu-Jitsu ・ Capoeira
Canada: Defendo ・ Okichitaw
PRC: Wushu ・ Sanshou
France: Canne de combat ・ Kinomichi ・ Savate
Germany: Universal Fight
Iran: Kung Fu To'a
Israel: Kapap ・ Krav Maga
Indonesia: Tarung Derajat
Japan: Judo ・ Japanese kickboxing ・ Karate (styles) ・ Puroresu ・ Shoot Boxing ・ Shooto ・ Shootfighting ・ Shoot wrestling
South Korea: Haidong Gumdo ・ Taekwondo
Norway: Stav
Philippines: Modern Arnis ・ Yawyan
Russia Russia: Sambo ・ Systema ・ Retuinskih's System ROSS ・ Ryabko's Systema ・ Aquathlon (underwater wrestling)
Serbia Serbia: Real Aikido
Thailand: Muay Thai ・ Krabi krabong
United Kingdom: Bartitsu ・ Catch wrestling ・ Defendu
Ukraine: Combat Hopak
USA: Chun Kuk Do ・ Jeet Kune Do ・ Kajukenbo ・ American kickboxing ・ Marine Corps Martial Arts Program ・ Modern Army Combatives ・ Collegiate Wrestling
There are various different style of martial arts that make available today.... the exciting Japanese martial arts styles that people around the world are training in those styles. Karate, Aikido, Kempo, and Kendo...
Tae kwon do is a martial art that in "todays" form of self defense has evolved by combining many different styles of martial arts that existed in Korea over the last 2,000 years and some martial arts styles from countries that surround Korea.
Today's Greco-Roman wrestling is one of the modern forms of competitive grappling. Judo is another popular grappling style.
Judo is of Japanese origin and has it's roots in Jiu Jitsu. One of the most heard about grappling styles is Jiu jitsu, the Brazilian form as practiced by the Gracies being the most publicized. Each style has something to offer...
Kickboxing has two words in it, kick and boxing. In the 1960's in the United States people with different martial arts backgrounds and together with some others developed a new style of martial arts. They had different backgrounds in boxing and karate. They made a new style and promoted tournaments through different organizations.
Mixed style is a description we use to describe art forms that have a combination of different styles of attack and defense. These use different combinations of hand and foot strikes with ground fighting techniques, or combine different arts to form a new art.
It is believed that elements of Chinese martial arts originated more than six thousand years ago as the first cavemen learned simple blocking and striking techniques to protect themselves. The first documented form of Chinese martial arts, traditional Chinese wrestling, is noted in the texts written by and about the legendary Yellow Emperor, Huang Ti, in the first half of the third millennium BCE.
That depends on what you mean. There are literally thousands of different martial arts if you put them into one category. The chinese alone has countless of different martial arts.
But you could put them into categories. Which I like to do sometimes. These different categories have their own style, their own philosophy to fighting.
Traditional martial arts: Karate, jui jutsi, kung fu, ninjutsu, wushu, wing chun etc. Traditional martial arts is not only about fighting. It's as much spiritual as it is physical. Typically these schools do not spar like MMA schools. I think it's wrong. Others disagree but each to their own.
Self defense martial arts: Keysi fighting method, krav maga, kali/eskrima, russian samba etc. These schools focus simply on self defense on the street. They study what usually happens and what the best way is to respond to it. The problem is that lately these schools have gained a lot of popularity and become watered down. Like krav maga for instance. Krav maga is used in the Israely military. No one will deny it's effectiveness in the military. But a watered down civilian version has popped up recently. It's based on the military one but it's not nearly as good.
Modern martial arts: MMA, boxing (I include boxing here), muay thai, bjj, kickboxing. Even though some of these are old and might be considered traditional martial arts I still put them in this category. What separates these styles from others is sparing. When you go to train, you go to train. It will be intense, it will be hard and it will difficult. Taking hits, getting hits. These styles build fighters. You won't go to class to contemplate on lives great mysteries, you won't get a 20 min lecture on discipline. You go to fight.
Again others have their own opinion about different martial arts. My opinion is seldom universal. But this is how I would organize things.
Defensive
Martial arts are of two types: combat and comtetive.
There are so many many martial arts that it's quate impossible for one to know 'em all.
Giving few names:
VARMA KALAI, NINJUTSU, BANDO, BANSHE, SILAT, KALI, SILAMBAM, KENDO, KEMPO, JIU JUTSU, NINJUTSU, THAI BOXING, KUNG-FU/GUNG-FU, WUSHU, SAVATE, AKIDO, FIVE ANIMAL FORM, JUDO, KARATE, TAE KWON DO, WING CHUN, JEET KUND DO, HAPKIDO, MIXED MARTIAL ARTS, MUAY THAI, BOXING, KICK BOXING, KRAV MEGA, BUTTHAN, ETC.
And what are they