Graffiti (singular graffito) were images placed on a surface in public view. The typical medium used was aerosol paint products. This form of self or group expression was usually done without permission of the surface's owner, with the intent of defacing the surface affected. Such activity was considered a crime in many jurisdictions, including on Deep Space 9. (DS9: "The Circle", "Crossfire")
Graffiti was visible on a metallic box beside an advertisement Hikaru Sulu, Montgomery Scott, and Dr. Leonard McCoy examined when trying to figure out how to make a whale tank while visiting San Francisco in 1986. More was seen on the window of a bus in which James T. Kirk and Spock rode. These graffiti markings were popular in the 20th century. (Star Trek IV: The Voyage Home)
Graffiti was also visible in an alleyway in 1996 Los Angeles. (VOY: "Future's End")
Graffiti was often used to convey a political message. Members of the Alliance for Global Unity did so by spraying the symbol of their group on Deep Space 9 in 2370. Their intent was to let both the Bajoran and Starfleet crew know of their presence. It was seen in at least two places on the station, including the door of Benjamin Sisko's crew quarters. (DS9: "The Homecoming", "The Circle")
Ojuy Gel was arrested in 2372 for spraying graffiti to protest the visit of First Minister Shakaar Edon to the station. Afterward, he was sentenced to three weeks of community service for his crime. (DS9: "Crossfire")
After a diplomatic misunderstanding on Gelrak V in 2380, some Gelrakians defaced the exterior hull and interior corridors of the USS Cerritos with crystal graffiti. A Starfleet Type 2 phaser could be used to remove it easily. (LD: "Temporal Edict")
