Graffiti has appeared in numerous games for various reasons. When it is used as texture work, it generally is indicative of a run-down or vandalized area, or a location where rebellious youth are found. In some cases, such as in Getting Up: Contents Under Pressure and the Jet Set Radio series, it is used as a core gameplay mechanic. In games like the Saints Row series or GTA: San Andreas, it may be used as a superfluous mechanic, or as a type of collectible. In at least one game, Sideway: New York, the game is entirely about living graffiti.
In all cases, it's reflective of the place in the real world for graffiti, which is a means of expression of everything from politics to one's own identity. Graffiti, also known as "tagging", is also featured in many FPS titles such as Counter-Strike in a way that's probably the truest to the real thing in that it can be original or reproduced artwork placed in interesting locations of a person's choosing for little or no true purpose other than to be noticed.