Situations would include:
Prize fighting
Beating people into submission, to either rob, interrogate, or intimidate them
Boxing
Fighting in towns (so the guards don't attack you)
Advantages to fighting unarmed:
Guards won't attack you in towns for brawling or don't respond with deadly force.
Its far more stealthy than guns
Bonus rewards to Reputation, and XP
Don't take a karma penalty when defeating an enemy with the same Karmic standing; for example if your a good guy, you can punch out another good guy without becoming evil. I mean, he's just unconscious, he'll get better.
Remember Mortal Combat, how after you defeated your oponent the words "FINISH HIM" would appear on screen; well V13 could implement options of things to do to your openent after you've beaten him senseless.