Know what your essential question is before you start. The essential question is the one you want answered (eg, Will you marry me?); everything else is a means to get the answer.
Using questions to clarify what the other person says shows that you are listening and often helps them to realise what they are saying themselves.
Start an inquiry with broad questions. These will help you find out more without revealing your assumptions. Unless you are testing subject-specific knowledge, they will also tell you more about the other person.
If you are trying to establish rapport, use questions that build on what the other person has said.
How you ask the question can be more important than what you ask. There are at least 10 ways of asking 'What do you want?', each with a different meaning.
Tangential and hypothetical questions help get a conversation out of a rut and encourage creative thinking. But if used too often, people might think you can't focus or are trying to be too clever.
If a question is not answered, let it go for the moment. It is generally wiser to come back to it later from a different angle than turn it into a big issue.
A list of questions helps organise a discussion with an unfocused group. Agree what needs to be answered and let them debate each question in turn.
The beautiful question begets the beautiful answer. If you don't like what you've heard, think up a different question before you blame the answer.