Randori (乱取り), (רנדורי), is a free-style practice or sparring, a Japanese term used in Ninjutsu and other martial arts. The term literally means "chaos against an opponent", and implies leaving the structured reactions dictated at the level of the kata.
Randori in martial arts vs. martial sports
The Randori in Ninjutsu and other martial arts is complex because of the multitude of techniques that are used and the lack of any restraining, martial sport, rules except maintaining safe practice.
The exact meaning of randori depends on the martial system it is used at. In judo and Shodokan Aikido, it most often refers to one-on-one sparring where partners attempt to resist and counter each other's techniques. In other styles of aikido, in particular Aikikai, it refers to a form of practice in which a designated aikidoka defends against multiple attackers in quick succession without knowing how they will attack or in what order. This form of randori is not sparring, and the attackers are not allowed to resist or attempt to counter the defender's techniques. It must be noted that the term is used only by Aikikai dojos outside Japan. In Japan, this form of practice is called Taninzu-gake(多人数掛け) which literally means multiple attackers.
Although in karate usually the word kumite is used for sparring, in some schools they also use the term randori for the "mock-combat" in which both karatekas move very fast, attempting and parrying acts of extreme violence with all four limbs (including knees, elbows, etc.) and yet never making other than the lightest contact. Total control of the body is necessary and therefore usually only the senior grades can practise randori. In these schools, the distinction between randori and kumite is that in randori the action is not interrupted when a successful technique is applied.
Randori may be contrasted with kata, as two potentially complementary types of training.
Analysis of Ninjutsu randori
Video of Randori during the 2012 Blitz