I know lots of people who like to sit in the CougarEat or Brigham Square and just watch people go by. Me too. In fact, I occasionally take it even further and I follow people around to see what they are doing and talking about. This is more tricky because they can't know you are following them. If they are hard to understand, I will sometimes walk in front of them and try to guess where they are going. This tactic usually doesn't work as well.
This being said, I do have a little respect for privacy, and if they are talking about something really personal, I don't listen in. However, I have taken detours for discussions of health-care, anti-matter, and literature. People are really interesting.
Speaking of interesting people, a friend showed me this link today. The first one is about a Mormon missionary. I've listened to 2 of them now and they were both amazing.