The famous French writer Marcel Proust periodically interviewed himself, with the following questions. These work very well as character questions, too, and it is for this reason that I list them here.
As you go down the list, think about how a specific character would answer the questions. Write down the answers, and keep them for future reference. Not all of these questions will be relevant to a particular story or character; not all the answers will necessarily show up in your story. However, the questions will help you create more rounded and believable characters.
You can, of course, do this with more than one character per story, too. In fact, I recommend that you think about using this questionnaire, or something like it, for all the major characters in your work.
* what do you consider your greatest achievement?
* what is your idea of perfect happiness?
* what is your current state of mind?
* what is your favorite occupation?
* what is your most treasured possession?
* what or who is the greatest love of your life?
* what is your favorite journey?
* what is your most marked characteristic?
* when and where were you the most happiest?
* what is it that you most dislike?
* what is your greatest fear?
* what is your greatest extravagance?
* which living person do you most despise?
* what is your greatest regret?
* which talent would you most like to have?
* where would you like to live?
* what do you regard as the lowest depth of misery?
* what is the quality you most like in a man?
* what is the quality you most like in a woman?
* what is the trait you most deplore in yourself?
* what is the trait you most deplore in others?
* what do you most value in your friends?
* who is your favorite hero of fiction?
* whose are your heroes in real life?
* which living person do you most admire?
* what do you consider the most overrated virtue?
* on what occasions do you lie?
* which words or phrases do you most overuse?
* if you could change one thing about yourself, what would it be?
* what are your favorite names?
* how would you like to die?
* if you were to die and come back as a person or thing, what do you think it would be?
* what is your motto?