Half the soundtrack is this, including Timesteps by Wendy Carlos, the Suicide Scherzo (an incredibly synthesized re-working of Beethoven's 9th Symphony, actually composed to glorify peace and universal brotherhood!), and the theme music itself.
Alex's face and voice as he tells his story; it's just as creepy as any of the acts of ultraviolence he commits.
The Ludovico treatment itself: imagine being put in a strait jacket, with your eyes held open by small hooks and having eye water put in your eyes every few seconds while watching video that eventually will make you sick! And you can't look away! Even actor Malcolm McDowell suffered some eye damage because of this treatment and developed a phobia of eyedrops that persists to this day.
Alex's torture at the hands of his former droogs, where he's beaten while his head is dunked in a pig's trough filled with water. Even more since it is a case of Leave the Camera Running, with actor Malcolm Mcdowell genuinely having his head dunked for a full minute. He later said that he was repulsed by the very smell of it after being forced to do 27 takes of it.
The final scene, where Alex envisages himself having sex with a girl, surrounded by 19th century type people applauding him. And then his mocking quote: "I was cured, all right!" For some reason... it's so weird, it's disturbing. And when he says "I was cured alright" he means he was cured of his "cure".
The most frightening aspect about this film doesn't even appear in the movie itself. There have in fact been people in real life who committed copy cat crimes, inspired by this film! Even Kubrick started to fear for his own safety and effectively banned the entire film in his adopted home country of England. It couldn't be seen in public for over 35 years, until his death.