Every person has a right, with just cause, to keep information secret. Secrets are necessary for society to function, whether they be Social Security Numbers or one's private thoughts. There is no universal right to every piece of information. To read someone's private information without just cause infringes upon one of the foundations of society and constitutes an unjust intrusion into another's interior life.
I might at first, but once I realized what it was I would stop. There likely isn't anything interesting there for me anyways. We are all taught from childhood that doing those types of things isn't right. So why do them? There is nothing for us to gain except satisfaction of curiosity.
I guess my view may stem from growing up in New York where you learn to mind your own business. I have no desire to view someone else's account information, especially if I don't know them. What is the point in intruding on someone's privacy. I personally would not want someone doing that to me under any circumstance. It is just bad karma.
No, you should not read through a user's personal information if you are mistakenly given access to their account. This information is of little significance to you if you do not know who the user is. In addition, if you try to use the information you can probably get into trouble. Because there is little that you can do with the information, there is no reason to read it.