HAL is generally creepy all throughout the film, but the sequence where he murders Frank Poole by ramming him with a space pod, severing his oxygen tube is outright terrifying, not least because it occurs both offscreen and in complete silence. Not to mention the extremely quick series of jump cuts into the lens of HAL's camera before Dave sees Frank go flying past the screen.
Related to this, some viewers noticed during HAL's game of chess with Poole, that HAL is cheating, announcing a wrong turn and even declaring victory when not in a position to do so. The computer they are trusting their lives on is able to lie!
His nearly silent, ruthless murder of the three hibernating crewmembers also definitely counts. "LIFE FUNCTIONS TERMINATED" will haunt your dreams.
The approach to the Monolith is one of the eeriest/creepiest scenes in film.
The famous "Beyond the Infinite" sequence is more awe-inspiring than scary, but when it's intercut with images of Dave FREAKING OUT, it gets really creepy.
Dave very slowly killing HAL by removing his memory. HAL's Creepy Monotone is enhanced when you realize that he is terrified and he can't even express it.
That damn Star Child at the end of the movie is pretty creepy, especially when he looks right at the audience. This troper was 13 the first time he saw it and didn't watch the movie again until college.