Not literally, but in a real--life way, yes. You can know what someone is thinking by their facial expressions, body language, and by the subtext of their words or actions. Of course, so often still, we are mistaken.
You can't read their mind, but you can read their expression in their eyes, their facial expressions, and their body language. As you are "reading their mind", watch their reactions and tailor your response accordingly. Of course, if you know the person, this is even easier. Once I was at a theme park with my son and we were eating lunch. A guy came up to the area and started doing magic tricks. He said he would read someone's mind. He looked at me, I raised an eyebrow, and looked him straight in the eye. He grinned, shook his head, and found somebody else. He could tell I wouldn't be an easy mark that day! (Usually, I am pretty gullible!)