Assuming I don't know the people, I get out of there ASAP or ignore them. Sometimes I'll argue after perceiving some kind of slight, but I'm relieved when it's over. If I'm not involved, I stay uninvolved.
Assuming I do know them, it can go different ways. As I'm a participant, I get fixated on being right. Take things personally. Insult the other person/people. Get louder as the argument goes on. Stand my ground until I wear them down or one of us has to leave. Later, I come back after cooling down, apologize and/or explain what my problem was. Oh, the embarrassment.
When people I know have a conflict that looks silly to me, I'll come in and instigate, sniping at both parties for my own amusement.
Person A: I don't believe it.
Person B: What's that mean?
Me: He's calling you a liar, B.
Person B: What?! No, you're the liar, A!
Then a few minutes later I'll do something similar to person B. If the drama is serious and people are getting hurt, I may try to mediate or (more likely) I will flee and hope they can work it out on their own.