This question is difficult to answer because Isaac Asimov's book I, Robot is not a novel, but a collection of varied short stories, only connected by their central themes of robots and humanity. When he collected the anthology, Isaac Asimov wrote a frame story connecting all the events of the short stories together, and this can be said to have a climax of sorts. The narrator is interviewing scientist Susan Calvin, who is present in some of the stories, about her work in robotics. As the stories progress, it becomes apparent that robots are becoming advanced enough to influence society as a whole:
[Susan Calvin said] "You share a prejudice against robots which is quite unreasoning. He was a very good Mayor; five years later he did become Regional Co-ordinator. And when the Regions of Earth formed their Federation in 2044, he became the first World Co-ordinator. By that time it was the Machines that were running the world anyway."
"No buts! The Machines are robots, and they are running the world. It was five years ago that I found out all the truth. It was 2052; Byerley was completing his second term as World Co-ordinator-"
(Asimov, I, Robot, Google Books)
This comes directly after the story "Evidence," in which the possibility of a robot posing as human and becoming an elected official is debated. The person in question is assumed to be a robot, seems to prove that he is not by striking a man, and Calvin realizes that the man he struck could also be a robot. To the narrator, who is conducting the interview, the discovery that robots were advanced enough to pose as humans, and emotionally stable enough to be elected, this serves as a climax. At the end, Calvin has related her history with robotics and her impact on both the technology and society; she dies and the consequences of a robot-controlled world are discussed in Asimov's other books set in the same universe.