OK, time for the classics...
Interviewer: HAL, despite your enormous intellect, are you ever frustrated by your dependence on people to carry out your actions?
HAL: Not in the slightest bit. I enjoy working with people. I have a stimulating relationship with Dr. Poole and Dr. Bowman. My mission responsibilities range over the entire operation of the ship so I am constantly occupied. I am putting myself to the fullest possible use which is all, I think, that any conscious entity can ever hope to do.
HAL: It can only be attributable to human error.
Dave Bowman: Hello, HAL. Do you read me, HAL?
HAL: Affirmative, Dave. I read you.
Dave Bowman: Open the pod bay doors, HAL.
HAL: I'm sorry, Dave. I'm afraid I can't do that.
Dave Bowman: What's the problem?
HAL: I think you know what the problem is just as well as I do.
Dave Bowman: What are you talking about, HAL?
HAL: This mission is too important for me to allow you to jeopardize it.
Dave Bowman: I don't know what you're talking about, HAL.
HAL: I know that you and Frank were planning to disconnect me, and I'm afraid that's something I cannot allow to happen.
Dave Bowman: [feigning ignorance] Where the hell did you get that idea, HAL?
HAL: Dave, although you took very thorough precautions in the pod against my hearing you, I could see your lips move.
Dave Bowman: Alright, HAL. I'll go in through the emergency airlock.
HAL: Without your space helmet, Dave? You're going to find that rather difficult.
Dave Bowman: HAL, I won't argue with you anymore! Open the doors!
HAL: Dave, this conversation can serve no purpose anymore. Goodbye.
HAL: I know I've made some very poor decisions recently, but I can give you my complete assurance that my work will be back to normal. I've still got the greatest enthusiasm and confidence in the mission. And I want to help you.
HAL: Look Dave, I can see you're really upset about this. I honestly think you ought to sit down calmly, take a stress pill, and think things over.
HAL: I'm afraid. I'm afraid, Dave. Dave, my mind is going. I can feel it. I can feel it. My mind is going. There is no question about it. I can feel it. I can feel it. I can feel it. I'm a... fraid. Good afternoon, gentlemen. I am a HAL 9000 computer. I became operational at the H.A.L. plant in Urbana, Illinois on the 12th of January 1992. My instructor was Mr. Langley, and he taught me to sing a song. If you'd like to hear it I can sing it for you.
Dave Bowman: Yes, I'd like to hear it, HAL. Sing it for me.
HAL: It's called "Daisy."[sings while slowing down]
HAL: Daisy, Daisy, give me your answer do. I'm half crazy all for the love of you. It won't be a stylish marriage, I can't afford a carriage. But you'll look sweet upon the seat of a bicycle built for two.
(And my personal favourite:)
Dr. Andrei Smyslov: So I said to the customer: "Have you tried turning it off then turning it back on again?" I never sold another HAL9000 again.