Interstellar Empires in Earth-777
The Kree Imperium
The Kree Empire has seen better days. Formerly the predominate interstellar society in Galaxy Prime (as the Guardians refer to it), over 80% of the Kree population was eradicated in the use of the Negabomb by the Kree Supreme Intelligence in order to restore the evolutionary progress of the race that had literally bio-engineered itself into a genetic dead end. This action resulted in the total economic collapse of the Kree Empire and the rise of the Merchant Houses into a position of predominance followed by the destruction of the Kree Supreme Intelligence. The rise of Ronan the Accuser, whose position was equivalent to Supreme Court Justice and Chief of the Secret Police, resulted in a return of stability to the Empire. The harvesting of the Phalanx's technology has brought about a Renassiance of Kree technological advancement as well (stagnated more than 20,000 years ago).
While the Kree Imperium is now down to a fraction of its former self, it still possesses one of the most powerful Navies in the galaxy and its defeat of the Annihilation Wave followed by Ultron has restored some sense of Kree self-respect. Ronan the Accuser briefly allowed the Green Lantern Corps to assist the Kree Empire against both Annihilus and Phalanx. He has since restored the barriers against them working in Kree space, arguing they can "take care of themselves." It is questionable if this policy will continue under the Inhumans but given Black Bolt's own opinions, it is likely the Green Lantern Corp will continue to be barred. Due to Richard Ryder's heroism during the Annihilation Events, The Nova Corps is now allowed to operate in Kree Space freely. Ronan, of course, has expressed a desire that any activities be handled primarily by Kree Nova Guardsmen. Richard Ryder is considered the exception to this rule due to his lengthy history of service to the Kree.
Of all the races in the galaxy, the Kree are most friendly with the Rann. While the Rann have never shared the Kree's love of conquest, their mutual love of science (and difficulties with genetic stagnation) has always been a shared point between them. The Rann alliance of worlds is minute compared to the Kree even in their diminished form but the two races have extensive pacts together. Ronan has reinforced their economic and military alliance while apologizing for their inability to help during the Rann-Thanagar war.
It is a bit analogous to Great Britain after the collapse of the Empire. Far weaker than before, but still quite capable of kicking ass.
The Skrull Empire
There's something to be said about turnabout being fair play. The Kree-Skrull war had lasted until Operation: Galactic Storm when the Skrulls watched their enemy decimated. The Skrulls then prepared themselves for a new campaign of conquest and subjugation. The Green Lantern Corps, the Nova Corps, and the Shi'ar were quite of the mind that the brutal monarchy would require all of their resources to repulse. Ironically, the Skrulls never got their chance to finish off the Kree or begin a new wave of infiltration and expansion. The hyperwave bomb by Skrull terrorists caused total panic across the Empire by stripping of their shapeshifting. More recently, the decimation of the Skrull Empire by Annihilus has effectively destroyed the Empire more thoroughly than even the Nega-Bomb did the Kree.
Bearing the brunt of the Nega-Zone invasion, the Skrulls are now an anarchic state. They have no military to speak of, the last being wasted in a futile symbolic gesture against the Earth in order to regain credibility withthe people. Their economy is all but destroyed and civil disorder is mixed with the threat of starvation. The throne is presently vacant. Even worse, the short lived theocratic regime of the Skrulls has collapsed with the deaths of not only the last Skrull Empress but also the murder of the Skrull gods by the demigod Hercules. The Green Lantern Corp is now patrolling the region as an unwelcome addition to the region.
L.E.G.I.O.N under Vril Dox II has made it a point to hire itself out to several petty Skrull warlords at unusually reduced prices. This is to prevent the total end of the Skrull race as a viable economic resource. Vril Dox calculates there's a 20% chance that the Skrull-Kree hybrid known as Hulkling may be able to reunite the remaining 10% of the former Skrull Empire into a thriving economic state.
The Shi'ar Empire
The Shi'ar Empire has always been a rising third power in the galaxy. Far more racially diverse than the Skrulls, Kree, and Rann; it counts many other species amongst its trading partners and was largely untouched by the Annihilation Wave. Thus it is possibly the most powerful state in the galaxy right now. However, even in its diminished form, the Kree are a credible challenge to that predominance and there are other powers nearly as strong like the Dominators and rising Rann Alliance.
Under Empress Lilandra, the Green Lantern Corps was allowed to operate in its sectors. The murderous D'Ken hated the Green Lantern Corp and was briefly allied with Sinestro in a plot to destroy them. Sinestro, of course, fully intended to use D'Ken then discard him but he was overthrown before any of Sinestro's schemes could reach fruition. Emperor-Consort Vulcan (also Military Supreme Commander---effectively making him Defacto Emperor since Deathbird cares nothing for ruling, only the title of Empress) has so far reserved judgment against the Green Lantern Corps. The Guardians of the Galaxy are aware Vulcan is a cruel and evil dictator with a taste for gladiator combat along with conquest. However, they've dealt with many such men over the years and are not antagonizing him while they're in their own weakened state.
L.E.G.I.O.N. is another matter entirely. Vulcan has been privately offering judicious bribes to Vril Dox in preparation for his wave of conquest planned against the Kree Imperium. Vril is fully willing to employ his forces services to garrison the world's conquered. Of course, he's also willing to work for the Kree as well....if the price is right.
(Vril Dox, CEO of Blackwater. Hehe).
The highly insular, murderous, and ruthless Dominator Empire recieved a bloody nose when it attempted to invade the planet Earth a decade ago. Since then, it's largely kept to itself. Dominators are long lived and patient, so they fully intend to take a thousand years or so until they can enact their next vengeance plan against the Earth for their recent humiliation. Oddly, the Dominators are not expansionist despite their militancy. Bluntly, Dominators are far too racist to tolerate conquering any other races and the very idea of long term association with them is so disgusting that they don't even want to take over worlds that have been previously inhabited by other sapient races. Thus, the Dominators mostly terraform and colonize other worlds while destroying any ships that choose to visit their space.
The Annihilation Wave was most pleasing to the Dominators and they've broken their traditional silence to welcome Annihilus' forces into the galaxy. This isn't because the Dominators are stupid. In fact, they know that Annihilus is far too nihilistic an enemy to be anything but a threat to them as well. The Dominators are just happy to see so many other species wiped out since that means the possibility that they'll eventually rise to replace them. They also think that Annihilus is more likely to overstretch and destroy himself if he's encouraged to bash himself against the other races. Being on the other side of the galaxy from the Annihilation Wave means they have little to lose.
The Dominators, of course, kill any Green Lanterns that enter in their territory. Being a yellow race, they don't have much to gain from association anyway. Even Sinestro failed to befriend them and made an "example" of one of their worlds as a lesson for showing him disrespect. The Dominators have a 800 year plan to blow up the Korugar for that one. Nova Corps soldiers are equally unwelcome in their lands.
The Rann Alliance
The Rann have long been a relative small force in the galaxy. Uninterested in conquest or expansion, they have been struggling with genetic decay for some generations now. Discovering a compatibility with human Earthlings, the Rann have decided to return to sexual breeding (as distasteful as that may be) with virile Earthmen to restore their gene pool to full random viability. Really, Adam Strange's heroism aside, it's going to be an awkward couple of diplomatic meetings when the cold fish of Rann come to Earth to ask for genetically viable male specimens to come have sex with their females.
In the meantime, the Rann have begun sharing their massive Technocracy's supply of technology with surrounding worlds. The Thanagarians joining their alliance with Prince Gavyn's Star Empire has drastically increased their power base. The Rann are actually rather trusted by everyone in the galaxy, except for the superstitious Thanagarians, for the fact that they haven't expressed interest in anything other than science in their entire racial history. The Rann have tried (and failed) to bring the Kree and Colu into their alliance.
The Rann were always friendly to Xandar and thus, the Nova Guard were always welcome in their territories. The destruction of Xandar was most distressing to the Rann and they're interested in the possibility of rebuilding the planet with the help of the Xandar worldmind (probably using cloning).
They're actually rather annoyed that Richard Ryder is endangering the World Mind by carting around the device and putting it in danger. They'd much rather construct a new facility for it and have candidates for the Nova Guard come to it for testing (while also providing their new Alliance with the opening share of new Nova Guardsmen). The Rann have no real issues with the Green Lantern Corps and have made friendly overtures to the reconstituted Guardians.