Robotic civilizations and artificial intelligence are a staple of science fiction but I cannot recall seeing any major, independent, and prosperous civilizations of robots (or artificial intelligences) in any of the Star Trek TV series.
By major, I mean something like the Federation or the Klingon Empire, but with robots/computers. To be more specific, it can be any civilization where one or more true general machine intelligences ultimately pull the strings.
Are there any?
In the Voyager episode, "Prototype", a race of robots are fighting another race of robots. Both of these races were built by biological civilisations who to fight their war with one another, but when they (the builders) made peace and tried to shut down the robot soldiers, the robots turned on them and destroyed them.
Also one of the robots seeks the ability to reproduce.
So it could be argued that these are races of robots, although maybe not strictly a "major civilisation".
There are two machine civilizations in Star Trek that I have heard of, and one is in canon and one is not in canon, and they are connected with similar sounding names.
In Star Trek: The Motion Picture, there is apparently a planet with a machine Civilization.
Spock sees an image of the Machine Planet in his spacewalk inside V'ger and later says:
SPOCK: I saw V'Ger's planet, a planet populated by living machines. Unbelievable technology. V'Ger has knowledge that spans this universe. And, yet with all this pure logic, ...V'Ger is barren, cold, no mystery, no beauty. I should have known.
Later they find the space probe Voyager VI inside V'ger:
KIRK: V-G-E-R ...V-O-Y-A-G-E-R ...Voyager! ...Voyager VI?
DECKER: NASA. National Aeronautics and Space Administration. Jim, this was launched more than three hundred years ago.
KIRK: Voyager series, designed to collect data and transmit it back to Earth.
DECKER: Voyager VI ...disappeared into what they used to call a black hole.
KIRK: It must have emerged sometime on the far side of the Galaxy and fell into the machine's planet's gravitational field.
SPOCK: The machine inhabiters found it to be one of their own kind, primitive yet kindred. They discovered its simple twentieth-century programming. Collect all data possible.
DECKER: Learn all that is learnable. Return that information to its Creator.
SPOCK (OC): Precisely, Mister Decker, the machines interpreted it literally.
SPOCK: They built this entire vessel so that Voyager could fulfil it's programming.
KIRK: And on its journey back it amassed so much knowledge, it achieved consciousness itself. It became a living thing.
Thus there should be a machine civilization with at least one planet, on the far side of the galaxy.
Some fan publications mention a machine civilization at Vega (Alpha Lyrae).
In James Blish's Cities in Flight series, Earth has defeated the Vegans who ruled much of the galaxy. Those Vegans probably roughly resembled Earth Humans, since Earthmen didn't consider them human but the non human civilizations did, and since John Amalfi, who was a little unusual looking, could have passed himself off as a Vegan if he wanted to, so obviously Earth legends don't describe the Vegans as looking like octopi, or dragons, or elephants, or cetaceans, or many armed Hindu gods, or centaurs, or centipedes, or other highly exotic beings.
At one point the narrator states that the Vegans were always defeated by humans because computers lacked the imagination to deal with human innovations; meaning that the biological Vegans relied on their computers for strategy and tactics.
In Blish's adaptation of "Tomorrow is Yesterday" Mr. Scott asks where the Enterprise could go to, since in that era the Vegans still ruled space, thus putting the Vegan Tyranny and the Earth-Vega war into the history of his Star Trek adaptations, if not necessarily into canonical Star Trek history.
Some Star Trek fan publications mention the Vegan Tyranny, and one (possibly Star Trek Maps, 1980) mentions that it is believed to have been a machine civilization. So they have misinterpreted the statement that the (biological) vegans relied on computers as a statement that they were computers.
So there are two machine civilizations in Star Trek that I have heard of, one connected with V'ger and one with Vega, and one is in Star Trek canon and the other is based on a misinterpretation of a statement which is not in Star Trek canon anyway.
Would the androids from "I, Mudd" qualify? They didn't have a lot to do when there wasn't a human around, but they were self-sufficient.
There was a great fanfic series called An Android's Tale that centered around the idea of the Mudd Androids joining the Federation. There was a new series of androids, the Joy series, that looked like Audrey Hepburn, because why not.
