In every GTA, you can use your fist in to bash up someone when you don't have a weapon, or you don't want to waste bullets on your target. In spite of the name 'fist', you can also use your feet to attack some one since the GTA III era. In GTA San Andreas and GTA Vice City Stories, you can learn several tactics to fight without weapons.
Naturally, your fist is not a pick-up and can always be used.
Although you're not entirely harmless without weapons, it's generally not a good idea to engage in a fight with only your physical strength to defend yourself.