There are several instances of badly behaving robots throughout Asimov's writings, but I am not aware of a standard, unmodified Asenion robot (programmed with the Three Laws) who could be considered malevolent. Some have unknowingly hurt or killed human beings (such as Hannis Gruer in The Naked Sun) or have behaved unexpectedly (Herbie from Liar!), but it would seem that correctly programmed Asenion robots are safe from direct action.
A recurring theme seems to be about the definition of a human being. There are several Asenion robots that have additional constraints, allowing them to violate the spirit of the laws. You must protect human beings? Change the definition of a human being. You must obey orders? Specify from whom the order must come.
The third example below is the only unmodified Asenion robot I could find that does not behave as it should. However, I would not go as far as to say he's malevolent.
In Foundation and Earth, the protagonists encounter a robot that is programmed to only obey certain people:
"We are programmed to obey Rulers only, Outworlder. You are not Rulers and not Solarian."
They're also angry:
"If you make difficulties, then we will partially inactivate you. We will damage you and you will then tell us what we want to know. [...] I am under detailed instructions," said the robot quietly. "I can do this. Of course, I shall do as little damage as is consistent with obtaining information."
They also seem not to care about the well-being of other humans:
"There is no Ruler Fallom. There is only a child and we have an excess of children. It will be destroyed."
Bliss said forcefully, "You dare not. It is a child!"
"It is not I," said the robot, "who will necessarily do the act and it is certainly not I who will make the decision. That is for the consensus of the Rulers. In times of child-excess, however, I know well what the decision will be."
This is a robot who :
- will refuse to obey a human being;
- will actively let harm come to a human being by snatching the child and delivering him to the Rulers;
- will let harm come to a human being through inaction by letting the Rulers kill him, and
- threatens physical violence to gather information.
The only explanation I can come up with is that it was only possible to allow 1) by constraining the definition of a human being (a Solarian with transducer lobes), which had the side effect of making the robots ignore the first law for everybody else. However, the robot does seem to still treat them as human beings, albeit without being concerned for their safety. I cannot explain the discrepancy.
What's a human?
In Robots and Empire, the protagonists find themselves talking to a female robot who doesn't think they are human:
The woman listened for a moment and then said, in an accent so thickly Solarian as to seem almost comic when coming from her perfectly shaped mouth, "You are not a human being."
She then flashed into action so quickly that Gladia, still some ten meters off, could not see in detail what had happened. She saw only a blur of motion and then D.G. lying on his back motionless and the woman standing there with his weapons, one in each hand.
She attacks one of the protagonists' robot while repeating "You are not a human being." I assume that she would have done the same to an actual human being. She then attacks all of them:
Landaree shouted in a stentorian contralto, "All of you. Join me! The two apparent males are not human beings. Destroy them without harming the female in any way."
Afterwards, Daneel was of the opinion that the robot would have killed Gladia, even though it had established that she was a human being:
"You fool! I was safe. She would not have harmed me."
Daneel said, "Madam, it distresses me to contradict you, but I think she would have done so as her urge to destroy me grew stronger."
Whether this is actually true is unknown. Daneel may have been mistaken, as the robot did not attempt to fire her weapon until after Gladia had been moved out of the way.
The explanation for her behaviour is rather simple:
"To the overseer, on the other hand, the key property of a human being was speech, Captain. The Solarian accent is a distinctive one and to the overseer something that looked like a human being was defined as a human being only if it spoke like a Solarian. Apparently, anything that looked like a human being but did not speak with a Solarian accent was to be destroyed without hesitation, as was any ship carrying such beings."
Harm vs. Orders
The last example I have is from The Robots of Dawn, where a robot has been instructed so strongly and expertly that obeying an order temporarily becomes more important than the safety of a human being:
The robot, seen as a darker shadow against the darkness, seemed a large one. He had, somehow, an air of capability about him. He said, "Your pardon, sir. Did you not have the company of two robots?"
"Gone," muttered Baley, acting as ill as he could and aware that it did not require acting. A brighter flash of the heavens made its way through the eyelids that were now half-open.
"Gone! Gone where, sir?" And then, as he waited for an answer, he said, "Are you ill, sir?" [...]
If the robot had been without special instruction, he would have responded to Baley's clear signs of illness before doing anything else. To have asked first about the robots implied hard and close-pressed directions as to their importance. [...]
"I am well. Don't concern yourself with me." It could not possibly have convinced an ordinary robot, but this one had been so intensified in connection with Daneel (obviously) that he accepted it.
The robot would end up leaving Baley in his dire situation, with no further hesitation:
He had forced robots to leave a patently unwell human being by playing on the force of the orders given them by a competent robot master who had been intent on strengthening the Second Law for his own purposes-and had done it to the point where Baley's own quite apparent lies had subordinated the First Law to it.
Whether this robot could be considered "malevolent" is unclear to me. It might have decided that Baley was not about to be harmed, as he was safe in a vehicle during what seems to be a storm of no unusual strength ("It was not a particularly bad storm, but to an Earthman it must have seemed overwhelming.") It might have concluded that Baley's distress was more psychological and that he was in no immediate danger.