This is a tough category. It includes co-workers going through a divorce, problems with kids or parents, drinking and drug use, health, etc. Sometimes just by listening you can be a comfort, or you may have gone through a similar situation and have some advice. Be very careful though.
Ask yourself if it is appropriate for you to help. How well do you know the person? How serious is the problem? Is there really anything you can do? Can you help with possible solutions? Be clear about work/personal boundaries and don't let people who really aren't your friends impose on you. And set limits on your emotional investment, before their problems become yours.
This is an area where the HR department may be able to help out. Serious problems like severe depression, drugs and drinking need to be dealt with by the professionals. Let them handle it.