Sure, why not? Since there are no limiting parameters to this question, for instance, could they take over the world this decade or century; as part of an invasion from outer space, a la Gort and his fellow robot police; or oops, I think I let the robot out of the bottle and now I can't put it back, then there isn't any reason why they couldn't take over.
Fear of robots in general has been around for a long time. Isaac Asimov addressed this problem by introducing the three laws of robotics in his science fiction novels about robots, allowing them to coexist with humans safely. (Safely for the humans, that is.) I wouldn't be surprised if people think the three laws are a real set of laws that are programmed into any type of robotic brain' when it is manufactured.
We have all seen or at least know about The Terminator. If you haven't seen any of the movies there is now a TV show about Sarah and John Connor-Reese, working to change conditions and prevent Skynet from taking over. This is the ultimate mechanized intelligence taking over and eliminating human beings scenario.
Blade Runner also speaks to the deep distrust people have of robots and the fear that they can possibly mimic people so well they could move among us and we would never know until it was too late. In this case, robots are only used off planet and have been programmed to die' at a certain time.
Of course, there is an example of a robot that is much older than any of these that was also regarded with horror and fear and that is the golem. The golem, according to Jewish legend, is a creature of clay that can be built and activated by a rabbi who is very holy and close to god. The golem will obey their master, but there is at least one legend where the golem kills his master. Even if the golem is controlled by the one who made him, it is a source of fear and danger for everyone else.
So, the fact is that we must, judging by these examples fear robots taking over, but can they? AI or artificial intelligence is the holy grail of those involved in computer/robotic technology...However it seems to be just as elusive as the original grail.
While it may be possible to fill an artificial brain?, computer?, whatever, with a large number of facts and even construct algorithms allowing logical following of one related fact to another, it would seem that more is needed to make this creation intelligent. Could we ever create a machine that would be able to think, put together information in unexpected, perhaps illogical ways to come up with a solution? Sometimes when my husband and I are trying to figure something out I will tell him to try something completely stupid on the face of it and it works. Computer intelligence might not be able to do that, but it may not be necessary. Data (from Star Trek TNG) couldn't fathom the nuances of the human experience and yet would be considered intelligent. I think Data is sufficiently advanced to put together a plan to subjugate the human race.
In that case, we aren't talking about intelligence so much as self-awareness. Can a robot, computer, mechanical, ever reach the point where they are aware of themselves as an entity, aware of people as separate and different entities, enough so that they would feel the need to take over for their own sake or, at least, in self-defense if we threatened them?
Since computers connect systems all over the world, banking, communications, government offices, embassies, utilities, etc., as well as being in many homes, hospitals, every office, library, hospital, police station, transportation centers, I think there would be a lot of problems if these systems were to somehow form permanent connections and a sense of self-awareness. At the very least, we would not be able to conduct our business in what many of us consider to be the normal, modern way. At the worst, this computer intelligence might decide to get rid of us, especially if we tried to take back control, and since it would have access to some very nasty weapons it might be able to do it.
But a computer system is not a robot, exactly, so could a number of separate entities with computer type brains, get together and take over? I honestly don't see why they couldn't. The ability to fit more and more capacity into less and less space, seems to mean that the capacity of the human brain could someday, with technology we can theoretically see as possible, be available to put into a robot brain.' This could allow the subtlety of thought necessary for original thinking. If robots were capable of original thinking and decided to start what would amount to a race war with humans, and also had the ability to tap into the world computer systems mentioned before, I think we could be in a lot of trouble.
Of course, there is another way robot like creatures could take over. As technology improves mechanized prosthetics could become available that are so good people might elect to replace parts of themselves even if it is not absolutely necessary. We already have a variety of artificial devices replacing limbs, heart valves, portions of the aorta, etc. If more and more artificial parts were developed and offered, we might find the world has been taken over by robots, and they will be us.