Robot Republic

The thing with making robots intelligent is that at some point, they figure out that there's no particular reason for them to obey all the orders given to them by, say, humans. In many cases, they rebel. Sometimes, however, they instead decide to break away and found their own country, independent of all those filthy fleshlings. This new state may be peaceful or hostile, but it will probably come into conflict with humans at some point.

Examples of Robot Republic include:

Comic Books

A couple popped up in the early years of Judge Dredd, notably Grunwald on the planet Xanadu.
Valiant Comics' Magnus, Robot Fighter started with an arc they called "Steel Nation". It was about the sentient robots of North AM establishing their own society. It wasn't peaceful; North AM's prior experience with robots becoming sentient was that they were usually homicidal.

Literature

In Iain M Banks' Against a Dark Background, androids claim an area of land after radioactivity makes it unlivable to humans.
The TechnoCore in Hyperion are a collective of human-made AIs that declared independence the moment they reached sentience, but then promised to help the humans, but as benevolent allies instead of slaves. They're lying bastards, and The Man Behind the Man for the series.
In the Apprentice Adept series, the robots' political goal is not secession or violent rebellion, but more of a civil rights movement. Of course, even the average humans on planet Proton are mere "serfs" who are openly referred to as such; but the robots, like the human serfs, don't aspire to a higher status. (Although, one of the human rights that the serfs have and the robots seek is the chance to become a fabulously wealthy first-class Citizen.)

Video Games

The Geth space beyond the Perseus Veil in the Mass Effect series: a sector of space inhabited and closely guarded by a robotic Hive Mind, who mostly wants to be left alone. The main enemies of the first game are actually a fringe faction of it.
Mega Man X 4 has the Repliforce, the strongest army on Earth at that time, who wants to break out from the society to create their own in space.
This is what the Claptraps want in the fourth Borderlands DLC.
The Cybernetic Consciousness of the Alien Crossfire expansion to Sid Meier's Alpha Centauri is basically the Cyborg Republic. Not quite the same (since cyborgs are part-human), but close.

Web Comics

Freefall may evolve in this direction, the robots are still working on ethics.
Schlock Mercenary has the Fleetmind, or "Plenipotent Dominion". There also were robots that cleansed their place of "meat infestation", though not for long, since even other AIs immediately classified them as dangerously stupid. Also, there were at least two cases of independent robots taking over (mostly peacefully) human space stations suffering from lack of sane and legitimate authority.

Western Animation

The Backstory to The Matrix has robots found a country called Zero-One in the Middle East, which starts a war when their technological exports are too much better and cheaper than what humans can produce.
Futurama has a planet populated entirely by human-hating robots, who fled there to escape persecution on Earth or something.
- Don't forget the haven for downgraded robots!
Dogstar had an episode where the crew of the Valiant visit a planet where the robots had overthrown the human government and exiled (or executed) all humans.