People's fears about question-and-answer sessions revolve around these worries:
You will lose control when you open the floor to questions.
You will get a question you are not prepared for.
You will have to answer whatever question comes along.
These fears vanish if you think of the question-and-answer session as something you control. The better your presentation is and the more direction you give the audience concerning questions, the more control you retain. Start by limiting the kinds of questions you have time for: "I will be dealing with questions that pertain to the subject I have covered." Laying the ground rules isn't defensive, it's a sign of organization and leadership. You're still the chosen speaker; you've been leading your audience throughout your speech, and that guidance should continue through the question-and-answer session.
In today's information age, it is impossible to have all the information on a given subject, especially if it's a broad one. As I stated earlier, there is nothing wrong with saying you don't know. But if you set boundaries and guidelines at the outset, you will limit the number of questions that fall outside your area of expertise.
Do you have to answer every question? No. If you feel you do have to catch everything, no matter how off-the-wall, you've already lost your leadership role. Set limits with grace, but set them. There is nothing wrong with telling someone his question isn't covered by your presentation, but that you would be glad to provide him with further information afterward. Your audience will respect you for it.
Banish these preconceptions about questions and you'll find yourself relaxing in spite of yourself. I've seen videotapes of people giving speeches and handling questions afterward; they look more comfortable during the question-and-answer sessions than during the speeches. That's not hard to understand; there is a naturalness to engaging in a dialogue that a speech can't match. Think of your audience as interested, not hostile, and you won't have to worry about what turn out to be good-natured dialogues.