Sports are one of the last refuges where physical altercations rarely get punished outside the league and if not acceptable under circumstances...are at least marginally tolerated on occasion. It's why NFL coaches seem to condone a few dust-ups in training camp; as long as no one gets more than a few bruises.
If you walked up to one of your coworkers and socked him in the face after he left a jam in the copier, your boss isn't going to pat you on the butt and say, "Walk it off!" Everyone is going to be freaked out, and you'll probably leave the office in handcuffs.
What makes a fight great in sports can't be pinned down to one specific set of circumstances or criteria—it's subjective. Sometimes a really violent brawl is elevated into the sports pantheon of great fights, but sometimes an awesome fight is special for reasons that have nothing to do with how many punches are landed.
Most people don't want to see a fight seriously injure someone or extend outside the comfort zone where the spectator suddenly becomes an unwilling participant.
Whether it's an epic mano-y-mano, old school fist-fight or a hilarious naive interpretation of what a proper butt-kicking entails—some of the greatest fist-fights in sports got the designation by standing out in their own unique way.