I train in Brazilian Jiu-Jitsu (purple belt), Judo (brown belt), and muay thai (doesn't use belts. I think these are the best martial arts for unarmed combat, but I'm biased. :-p
Karate is basically a system of hitting people which originated on the island of Okinawa. The island was invaded several times due to its strategic position between China and Japan. Karate was greatly influenced by the martial arts from China. However, it was further developed during Japanese rule when they forbid native Okinawans to own weapons.
A Ninja is basically a Japanese word for a spy. Ninjutsu is the training of a ninja; although, there isn't really a single style of martial arts that ninjas study. Nobody studies authentic ninjutsu anymore. Anyone who claims to is a fraud. Any modern "ninjutsu" systems are reconstructed based on someone's "best guesses" of what ninjutsu actually was. I am not a fan of most ninjutsu schools in North America.
Judo is the first "modern" martial art. It was founded in 1882 by a Japanese scholar named Kano. In Japan there were many types of martial arts called "jujutsu." Some had practical techniques, some did not. Kano took the most effective techniques from each style and changed more techniques to be more effective. Kano came up with ways to practice in realistic situations (one way is called randori - aka free sparring). He also invented the standard uniform (called a gi - the usually white uniform that looks like a bath robe), and he invented the usage of different colored belts to denote how skilled one was in the martial art. Therefore, Kano was the first to rank his students with black belts and others. Judo is famous for its very effective takedowns and throws. It was adopted as the official style of the Tokyo Police Force and greatly influenced virtually every other martial art in the world. Judo has also been adapted as an Olympic Sport too.
Brazilian Jiu-Jitsu (my style) is based on judo combined with several other martial arts in Brazil. It specializes in ground fighting, joint attacks, and chokes. BJJ fighters became famous through great performances in mixed-martial arts fights. The UFC was started by BJJ fighters, and now most fighters include some form of BJJ in their training regime.
Aikido (not aikaido) is a "soft" martial art founded in the early 20th century. Unlike judo or BJJ, aikido's philosphy is against competition. They put most emphansis on spiritural development. This is what I mean by "soft." While judo literally means "the way of maximum efficency with minimum effort," aikido literally means "the way of energy." They believe in using one's "mystical" energy to deflect attacks. Aikido is generally known for good wrist-breaking techniques. I use some aikido techniques and philosophies in my martial arts, but I am not a big fan of aikido in general. I don't feel it is as effective as BJJ or judo.
Kung fu is literally Chinese for "very skilled." So one can have kung fu in anything, technically. As commonly used in North America, Kung fu is slang for Chinese martial arts. The most common of which are "wing chun" and "shaolin" martial arts. Shaolin martial arts are greatly influcenced by the religion of Buddhism. These are older martial arts with religious or nature-influenced techniques. Several forms are named after animals. Wing chun is the first martial art Bruce Lee studied. It is a striking martial art similar to karate, but focusing more on circlar movements (while karate is more linear). There is no official ranking system in this martial art.
Taekwondo is a striking martial art from Korea. It was invented in the mid-20th centruy from karate (introduced during the Japanese invasion in WW2) and several traditional Korean martial arts. It focuses more on kicks than karate, but it is still very similar. TKD is also an Olympic Sport focusing on scoring as many "hits" as possible. For this reason, Olympic TKD is often called "point sparring" and is not very useful for self-defense. The other type of TKD can be useful for self defense, but I prefer muay thai kickboxing (another martial art known for kicking, but from Thailand) combined with western boxing.
Krav Maga is a type of martial art from Israel which focuses on giving "no mercy" to your opponent. It adapts techiques from many other martial arts in worst-case senereos. Krav Maga was invented in the early-to-mid 20th century to protect the jewish community in Europe. Krav maga focuses on both unarmed and armed combat situations.
Won ton is a type of soup. LOL
Chai tea is a type of beverage. HAHA Tai Chi is a soft martial art like aikido that focuses on channeling one's "mystical" energy called chi. The types of energy are represented by the "yin-yang" diagram that is commonly known. It looks a lot like Worf's martial arts classes in TNG. I'm not a fan of Tai Chi, myself, because I don't believe chi exists.
I have no idea what rip torn is.