Nope. The only times I would consider it is if the person were threatening the work place or someone at the workplace or if it was a serious breach of policy (even then, I'd probably do something else, rather than tell my boss).
For instance, I used to work at a company that had a contract with a local hospital. My office was in the hospital in the admittance/financial counseling offices. One of my coworkers (well, hospital employee) posted on her facebook that a very prominent businessman in our city came in for chemo. So not only did she say he was there, but she said what for. I don't know what possessed her to think this was ok. Somehow (not sure if a coworker snitched or what) the manager of that area found out and had to call the businessman and explain and apologize. He was very gracious (he is deceased now, but was known for being a very good man - one story said that he asked one of his employees to go to lunch with him and then flew them to another city on his helicopter), but the employee was fired. I don't think it went further than the firing, but it certainly could have.
