Ask a celebrity, especially a high-profile one, questions about his current projects and how he got to where he is now. However, avoid asking questions pertaining to what might be said in the tabloids because, in the end, Angelina Jolie and/or Brad Pitt might as well walk away from the interview immediately.
Obviously, not all celebrities had such a glitzy, gossip-laden lifestyle before they became famous. Therefore, don't hesitate to ask them about their humble beginnings. You may learn something about your own struggles in life in the process.
If a celebrity's "beginning" or "end" happened to be filled with Shakespearean tragedies or other traumatic events, you should try to be as subtle as possible. For example, if you asked actor Ryan O' Neal about former lover Farrah Fawcett's cancer treatment in graphic detail, he'll probably start crying because it will bring back painful memories for him. Therefore, you should ask him if he ever got over his loss before you move on with the interview.
If a celebrity is in the middle of a high-profile breakup or ultra-expensive divorce, a la Madonna and Guy Ritchie, try asking her how she is coping. Again, asking a celebrity about his or her personal life can be emotionally draining, making this a slightly tricky ordeal for both the interviewer and the interviewee. But what both parties can learn in the process is something about human nature itself.
If a celebrity has been accused of a major crime, a la O.J. Simpson, try avoiding the subject altogether.