There are two main factions - the Union and the Confederacy.
The Union is a conglomeration of various worlds and countries, more or less dedicated to trying to keep themselves safe. Membership into the Union requires free passage between the various states, countries and worlds for law-abiding citizens as well as a contribution in terms of resources (according to the ability to give) to the common defense and welfare. In general the rights of sentients are considered of paramount importance by the Union, and though some areas are ruled by monarchies and dictatorships, democracy is in general the rule of the day, and those areas under dictatorships had best treat their citizens nicely and allow them to leave if they see fit, lest they be booted out. The Union is headed by a legislature and an executive council which executes policy. Further, the Union has a powerful military wing, which fights to protect its citizens. The Union's military wing also has a number of affiliated members who, though not directly under military control, nevertheless assist in help when needed. Most 'wandering heros' fall into this category. Although the Union does much to defend the rights of sentients, even those not in this quasi-mega-nation, they are well aware of the necessities of warfare, and are willing to take aggressive steps when necessary, including attacking enemy "civilians", executing enemy prisoners, and beating information out of prisoners should the conditions warrant. Though this is not usually standard practice, it does happen and is an accepted fact.
The Confederacy on the other hand are the 'bad guys'. In general the Confederacy is a lose organization of countries, individuals, empires and other such organizations that are bent on destroying the Union. The Confederacy's military and civilian lines as a whole are somewhat indistinct - it is difficult to tell just where one begins and one ends. Almost all in the Confederacy are in this for their own goals - desire to take over the world is not unique and it's almost certain that should the Union ever fall the Confederacy would immediately be plunged into self-destructive civil war for control. Military discipline is harsh, civilian casualties are usually acceptable, and the rights of sentients are marginal at best, usually being that the strong survive. Surprisingly, though, like the Union, the Confederacy is also comprised of a Council, albeit the Council is often embroiled in its own backstabbing politics, leaving the military to its own devices. Nevertheless the Council controls resources sufficiently such that the military will continue to bend to its will (although in truth the military has by nature a fairly broad amount of discression at its own disposal so long as it keeps the Confederacy solvent and the Council happy).
Most characters should fit into either the Union or the Confederacy. Many worlds will have part of their territory taken by one or the other. The Union's capital city is New Washington, located on the East Coast of one of the Americas in the Strait of the Americas. The Confederacy's capital city is New Pyongyang, located on the Korean Peninsula on a copy of Earth about 250,000 miles southwest of the Union's capital city - not too far considering the methods of transportation employed.
There are other factions present - the Unified world is staggering in size - but these are the main two for the part of the MUSH that is used. Other small factions may be added as time goes by, but large ones will likely be TP only in nature. There is a third "faction" of note within the Multiverse.
The Cirrus-Marine Pact
When the Union and Confederacy were forming from the splintered "proto-factions" that each was born from, a smaller, third faction formed under the Cirrus-Marine Pact. It consisted almost entirely of a group of nations from worlds that were either neutral from the start, or grew tired of being involved in the war effort and split off from the proto-factions. Swearing non-aggression to the superfactions, and promising not to favor one over the other in trade matters so long as the Union and Confederacy did not do them harm, the members of the Cirrus-Marine pact were left to their own devices. Their "twin" capitols are Cirrus and Marine Cities, located in the western part of the Great Ocean. Although they are not as strong as either the Union or Confederacy, the collective resources and forces of Cirrus-Marine are considerable and no single world has the manpower required to do them permanent harm -- nonetheless, unlike New Pyonyang and New Washington, their capitols are much more readily assailable, even if a prolonged attack would be paid with by blood.
Cirrus-Marine's citizens enjoy freedom comparable to that of the Union, but there is some measure of censorship within the media in order to avoid seriously provoking one of the larger powers -- more noteably the Confederacy, which has on rare occasion given the neutral territories trouble. Cirrus-Marine's government is a democracy, and they maintain a significant defensive force. Were Cirrus-Marine to join with one of the larger factions, they would provide a significant advantage in the war effort, and their territories frequently use this to their advantage, primarily for leverage against the Confederacy.
Note: While apping into Cirrus-Marine as a civilian, or as a part of it's defensive force is possible, it is inadvisable to do so. They're going to see a lot less action because most nations in the Cirrus-Marine Pact want to stay neutral, and going directly against that goal can get you dishonorably discharged, and booted from their territories entirely if you piss off the wrong people.