If you want your interview to be truly definitive, you need to know what others have written about your subject. The piece resulting from your interview can't ignore certain constant topics surrounding your subject, but you want to break new ground and reveal a side of the subject that hasn't gotten much attention.
Avoid questions of simple fact, such as those beginning with "what," "when," and "where," except as follow-up questions. Begin instead with "how," "why" or "tell me about..." For example, "How did you meet your spouse?" is not often answered with one or two words and could be enough to get your subject talking. Try to anticipate when the subject would answer yes or no and rephrase the question into an open-ended question.
A person's life changes will often present opportunities for new topics, or exploring old topics in a new way. Use anniversaries to prompt both a retrospective and a forward look. Another strategy is to take a seminal event and ask what the subject learned from it.
If your subject has gone on record refusing to discuss a topic and the refusal is not for legal or confidentiality reasons, consider offering a sympathetic ear: "I know a lot has been said in the media about X, to the point that I'm guessing you distrust any question about it. But is there any aspect of the situation that you feel has not been fairly presented? Here's a chance to present your side." Respect the subject's answer. Ask follow-up questions so you understand the subject's point of view and report the answer objectively. Do not slant it.
Sometimes all you need to keep the conversation flowing is ask, "How so?" or "What do you mean by...?" Ask fact questions, such as "when" and "where," only if you need clarification. Sometimes a simple fact question will prompt a rambling answer or stop the flow of conversation. A fact question can be followed with a why question.
Sometimes the best part of the interview will occur when the subject thinks it's almost over. Many a reporter has closed her notebook and stood up, only to hear new topics and great quotes. At the end of the interview, you might ask "What should I have asked that I didn't?" or simply "How did I do?"