The Bern Monarchy: Following the Battle of Endor, the Empire was dealt what appeared to a be a mortal blow, but things are never, of course, so simple. Much of the Imperial citizenry--especially the military--saw themselves as the heirs of a glorious tradition stretching back thousands of years into the age of the Old Republic. If Palpatine was a bad seed, well that didn't invalidate generation after generation of tradition, and Palpatine was ancient when he died anyway. Surrendering to barbarians, anarchists and malcontents--as they saw the Rebel Alliance--or the traitors who colluded with them in the old Senate and elsewhere, was never going to happen. Seeing themselves as the heir to the Old Republic through the unfortunate hiccup of the Empire, this ancient tradition evolved into the Monarchy. While not nearly as vast as during the heyday of the Old Republic, the Monarchy is still one of the largest and strongest of the superpowers in the galaxy. Protected by the Gray Marshals, paramilitary agents capable of standing toe to toe with Sith or Jedi when they were founded, the Monarchy is well-provided for with it's own Force and lightsaber wielding Knightly tradition.
The Revanchist Republic: The direct heir of the New Republic established by Mon Mothma, Leia Organa, and the rest of the architects of the Rebel Alliance, the Republic had many generations of hardship. While many of the Rebels were well-meaning idealists who wanted nothing more than a restoration to the way things were before Palpatine, it was clear that too many in the Rebel Alliance were little more than scoundrels, pirates, and other opportunists who took advantage of the chaos of the Galactic Civil War to line their pockets with what plunder and pillage they could. Following short periods of relative peace, the Republic was plagued by periods of violence and anarchy, not unlike an extended comparison with France following the overthrow of the Bourbon monarchs. After being reduced to a mere handful of Core worlds, the Republic finally got its act together and started aggressively retaking former territory, "liberating it" from whatever "tyranny" might have been occupying it. This revanchist policy has been adopted officially as its new name, the Revanchist Republic, an emerging, feisty superpower--not really a rival yet to the Monarchy or the Empire, but a growing power nonetheless.
The Sith Empire: Centered on the ancient capital of Dromund Kaas, the Sith Empire may be the most powerful polity in the galaxy--although that often works to its disadvantage when no other group trusts them, ad they are often "ganged up on" both diplomatically and militarily by wary other governments who find tenuous alliance in restraining the ambition of the Sith. But the Sith are patient in their ambition to rule the entire galaxy, and are seemingly content to hold strongly to their existing territory and advance slowly over their opponents over the course of generations. Black-garbed Sith soldiers bring a measure of order to the galaxy, or at least so say the Empire's apologists. And drawing from the ranks of both Sith acolytes as well as their allies the Nightsisters and Nightbrothers, the ranks of Force-using knights who serve the Empire's interests is considerable.
The Corporate Sector: In the chaos of the Dark Age, many large corporations were more stable and less corrupt than most governments. And in a large reach of the Inner Realm worlds, the corporations essentially became the government. Providing a high quality of life to those citizens willing to, in a way, combine civil service and their careers together, the Corporate Sector has beat back all attempts by traditional governments to integrate them fully. Protected by vast droid armies and loosely allied with the many knights of the Cyborg Order, the Corporate Sector may indeed be mercenary--by definition even--but that doesn't mean that they're more corrupt or heavy-handed than any other government. The watchword of the Corporate citizens is professionalism in all aspects of life.
Hutt Cartel: Infamous as making up the dark tentacles of a seedy underworld throughout much of the rest of the galaxy, there also is a patch of the galaxy where the Hutt's rule as undisputed masters continues as it has, indeed, without change for millenia. Rather than strong traditional military, the Hutt's have relied on each Hutt master's private militia, often consisting of eclectic and unusual companies of mercenaries. While this disunity might be seen as weakness, and certainly the Hutt's engaged in few overt acts of conquest or military adventurism, in reality the Hutt's maintain a strong enough presence that their place has not been seriously threatened in generations.
The Mandalorian Arm: Following the disastrous collapse of Duchess Satine's well-meaning but foolishly naive pacifist regime, the Mandalorians looked more to their glorious and storied warrior past on which to model their society. Death Watch themselves were still seen as an equally dangerous extreme as Satine's pacifism, yet the evolving Mandalorian society grew to resemble Death Watch more than many realized. Initially allied strongly with the Hutts, the Mandalorian Arm--so known because its territory is centered on one of the spiral arms of the galaxy--has grown in power and prestige so that it can treat with the other Great Powers as an equal. Although some Mandalorians are born with the genetic predisposition to be Knights (as are most groups in the galaxy), there is no real tradition of force-user training amongst them. Rather, a fully trained and equipped Mandalorian supercommando can fairly be considered the equal of any Knight in combat without using the Force--a point of pride for Mandalorian soldiers.