Martial arts are arts of combat or self-defense.

The gymnasium on board the Galaxy-class starship had martial arts areas. (TNG: "Clues", "Second Chances")

Tuvok had extensive training in the martial arts of many Alpha Quadrant cultures. He knew of over 94 ways of killing someone using only a finger, a hand, or a foot. (VOY: "Meld")

Jadzia Dax was an expert in Klingon martial arts. (DS9: "Facets")

Human

• Aikido
• Anbo-jytsu
• Boxing
• Kickboxing
• Sumo
• Tai chi chuan
• Wrestling

Klingon

• Calisthenics
• Gik'tal (fake)
• Mok'bara

Norcadian

• Tsunkatse

Vulcan

• Suus Mahna
• tal-shaya
• Vulcan nerve pinch (neuropressure)

Other

• Galeo-Manada (possibly Ktarian)