The fist represents the unarmed state for the protagonist; he will not draw attention in weapons-free zones, and merely locking onto pedestrians or police will not result in any physical action which might cause a panic or attract a Wanted level. In some GTA games, fists can be augmented with Brass Knuckles to increase damage.
Naturally, fists are a last-resort weapon in the GTA games, lacking the range of firearms and power of melee weapons. Bare-handed attacks have unique properties -- for example, they can be chained, causing the protagonist to unleash a series of various punches and kicks, including a stomp or ground-level kick if an enemy is lying prone. In Grand Theft Auto: San Andreas, the player is able to learn more powerful moves by fighting and defeating gym trainers. Grand Theft Auto: Vice City Stories introduced new abilities while fistfighting, including breaking opponents' necks. In the Grand Theft Auto IV era, fighting was made more realisitic, and timing elements were introduced into physical combat to allow dodging and 'finishing' moves. While there is almost never a need to fight barehanded in multiplayer, fist fights are often fun.