Perpetual
A Perpetual is a person of the grim darkness of the 41st millenium who drew the absolutely shortest straw possible: they are immortal. And nothing of this "age without youth" or "immortality without indestructibility" bullshit: they do not age and can survive the most gruesome deaths imaginable up to and including taking an Exterminatus to the face because they can reassemble themselves from their constituent atoms. They're like Wolverine on steroids like that. Which, given the relentless sunshine of the Warhammer 40.000 universe is NOT a good thing: not even death will relieve your suffering. There are only a few things that can kill a Perpetual for good, but these powers and weapons are known to only a few individuals in the galaxy (and even then it's not known for certain how effective they are, or if they even work). Very little is known about the Perpetuals including their origin, number, purpose or even if those suspected to be them actually being Perpetuals (all that we know is that durning the Horus Heresy, there were exactly 3 Perpetuals living in Ultramar; given that Ultramar consisted of 500 planets at the time, we have to assume that they're extraordinarily rare). Of only eight individuals is the status of Perpetual known or confirmed.
We do however know, that people could be turned Perpetual by being resurrected. Which, ironically, might imply that Kharn and Lucius at some point became Perpetual too, since they're both came back from dead. It'll explain how Kharn managed to survive for that long despite his suicidal psychotic charges into everything he sees, and how Lucius resurrected without possessing anyone's body after being cut too pieces by an emotionless Rubric Swordmaster.
The Emperor
With all of his mysteries it would explain a number of things about the Emperor if he was a Perpetual: his age, knowledge in an era where everyone else on Terra was too busy LARPing a crossover of Terminator and Fist of the North Star to learn shit and his massive power (learned over time). On the other hand it would not explain why he didn't just regenerate after being bitchslapped by Horus. The best explanation for this is that that the Golden Throne, while maintaining his life functions, is also keeping him from resurrecting himself- in theory, if it was shut down, the only real effect it would have is that the Emperor would "die" for a day or two at most before fully healing from his injuries. A shame that nobody seems to realize this, as it would end most of the Imperium's problems on the spot, and would create some new ones, as quite a few people wouldn't be happy with the return of Imperial Truth, especially the Ecclesiarchy. Of course, knowing the Emperor he'd crush them like bugs if they tried to oppose him, or even if they didn't. There is no way he would agree with the current Imperium.
Recent revelations from the Horus Heresy books also suggest that his godlike powers were actually stolen from the Chaos Gods themselves instead of being wholly his own. Needless to say, the Ruinous Powers still have a grudge.
Ollanius Persson
A confirmed Perpetual, ol' Ollie Persson was one of the Argonauts of Greek myth and fought at Austerlitz (during Napoleon's conquests) and Verdun (infamous as one of the bloodiest battles in all of World War I). It also explains how he managed to survive boarding Horus' flagship during the Siege of Terra. It is unknown if Horus actually managed to kill him: while CHAOS MINDBULLETS certainly sound like they could do the trick it still is quite possible that he reassembled himself and walked off, not giving a fuck. A man with true balls of steel.
John Grammaticus
Agent of the Cabal and a lesser psyker; John Grammaticus WHO WAS GORDON GRAMMATICUS' BROTHER WAS ONE DAY AT AN OFFICE TYPING ON A COMPUTOR is an interesting case: after he died at Anatol Hive an Eldar Autarch called Slau Dha found his body and made him into a Perpetual, signaling that it is possible for humans to become Perpetuals. That, or Slau Dha was the equivalent of Ramirez and John was Connor MacLeod from Highlander. If this were the case this would make John and Slau Dha at least eight times more awesome. Grammaticus' skills gained over the course of a millennium of life were instrumental for recruiting Alpharius to the cause of the Cabal, but he felt bad for this and stepped out of an airlock in the faint hope that it would kill him. (It did, but then he just came back to life again.)
After the dropsite massacre he spent some time digging up an old relic spear that was actually made from cast-off lightning of the Emperor's divinity, reputed to be able to kill anything, even other immortals. After the apparent failure of the "Alpharius Gambit" (two choices, two primarchs, go figure) the Cabal had intended to use it to stop Vulkan from reaching Terra and interfering with their future plans.
Unfortunately such a powerful relic made Grammaticus into a big giant target, and he ended up getting captured, killed and recaptured by the Word Bearers and the broken legions and eventually finding his way to Macragge.
On the way he was contacted psychically by this dick who told him that he could strike back at the Cabal by stabbing Vulkan himself, since if another immortal did it it would work differently, and in this case it would somehow heal the primarch who was mentally broken after years of torture by Konrad Curze. Because of reasons.
Also at some point during the invasion of Calth he found Oll Persson and tried to recruit him to the cause, though that didn't go too well as he was only half-hearted in his attempts anyway, plus Oll couldn't be bothered.
So after seeking Vulkan out on Macragge he stabbed him, investing his own immortality into the strike, and sucking it out of himself and making him mortal... also apparently killing Vulkan properly this time and therefore doing what the Cabal wanted in the first place.
It is now uncertain what Eldrad actually intended, either Vulkan will regenerate or become something entirely new or is just plain dead and Eldrad just double-reverse-psychology to get what he wanted and Grammaticus was just a sucker.
Damon Prytanis
Another agent of the Cabal, though unlike John Grammaticus, Damon was more of a soldier than a spy and got all the killy jobs. It is heavily implied that he was the one who killed Martin Luther King as well as other important figures throughout human history.
Was apparently more comfortable with his position in the Cabal, even though it meant working against his own species, and would infer as much during his meetings with John Grammaticus, which made him more trustworthy in the eyes of the Cabal. During John's last mission Damon was sent to watch over him and make sure that he didn't falter or chicken out and try to derail their plans.
He was the individual who brought Cyrene Valantion into the Cabal's fold, having to die once or twice on board the Word Bearer's starship just to prove a point to her.
Vulkan
Like his dad probably was, Vulkan of the Salamanders was a confirmed Perpetual. This was put to the ultimate test by none other than the goddamn Night Haunter himself, who proceeded to perform the most depraved tortures and murders on the Lord of the Salamanders in an attempt to break his will. Whether he was shot at with bolters at point-blank range, cut apart, decapitated, eviscerated, impaled, dismembered, evaporated, getting his throat torn out with a rusty fork, being quite literally mindfucked,or being tossed naked out of an airlock, Vulkan would neither break nor die, pissing Curze right the fuck off. Eventually Curze locked him in a maze courtesy of Perturabo where he would hunt Vulkan himself. Curze's mistake was to place Dawnbringer at the center of the maze; when Vulkan got to his hammer he activated a built-in teleporter that sent him right over to Macragge where he promptly burned up in the atmosphere like a human meteor, re-killing him in the process.
Here things get complicated: Vulkan regenerated on Macragge but lost his mind, so Guilliman kept him locked up until he could figure out what to do with him (even concealing his presence when the Lion arrived). However, when Konrad Curze arrived on Macragge after stowing away on the Lion's flagship, Vulkan escaped in a moment of lucidity and tore his way across the planet (while naked) hunting Curze down and almost defeated him in a one-on-one duel. Shortly afterwards John Grammaticus found the broken primarch and stabbed him with the Fulgurite, a spear once belonging to the Emperor himself and charged with his psychic essence. He could not regenerate from this and neither could Roboute Guilliman, Sanguinius or Lion El'Jonson remove the spear from their brother's chest. Given that he was made a casket and send back to Nocturne for burial we are forced to assume that this casket included a long tube-shaped appendage at least several feet long sticking out at an unusual angle, making this (while tragic) at least eight times more amusing (assuming that he was ever stabbed in the first place).
Guilliman was hopeful that Vulkan would resurrect himself in time, and insisted that the coffin was a preservation capsule, which Guilliman dubbed "The Unbound Flame". Some Salamanders who maintained a vigil of mourning thought they could hear a heartbeat. Interesting is that The Unbound Flame is one of the nine artifacts of Vulkan searched after by the Forgefathers and is, here comes the important part, one of the four that is NOT in their possession yet. So this makes the issue even more complicated or someone stole The Unbound Flame and added it to his private collection.
What raises an interesting question in Vulkan's case is regarding the source of his powers. If it was given to him by the Emperor, it begs the question why the Emperor did not give all of his sons this ability (though it sort of answers itself with the thought of Angron becoming the Juggernaut (bitch!). If it was not the case, it would suggest that the Perpetual trait can be passed down one's bloodline, or at least transferred by cloning. Lots of Big E's abilities apparently can be passed to his 'sons' but we'll never know if he intended to pass some of them (magic powers and immortality specifically) to all of them or not.
Certainly Vulkan was probably the nicest of the primarch and as such would probably have been the best bet for an undying son. When Empy was looking over the petri dishes for which one to add the immortality to he had to choose between (in order): a two faced jerk, a preening egotistical asshole, a genocidal maniac with poor impulse control, Genghis khan, a frothing berserker, a stubborn joyless misanthrope, a psychopath, a guy with a terrible terrible secret, a nerd who'd rather be talking to a toaster, a psychopath, an aspie, a psychopath, a massively powerful psyker who can't take orders, a massive dick, a petulant child, a nice guy and two people obsessed with secrets and lies, on the other hand a lot of those traits were nurture rather then purely nature. Even so, if he did do it deliberately, he made a decent choice.
Anval Thawn
Justicar Anval Thawn of the Grey Knights is the biggest mystery of them all. All that is known is that he can walk away from the most gruesome Daemon-inflicted deaths one can imagine, much to the chagrin of his brothers and bewilderment of the Brotherhood's Librarians. It also begs the question of why him being a Perpetual was not detected during his induction into the Grey Knights, either during the tests or abnormal restoring from the involved chiurgery or the speed at which he accepted the nineteen organs. Perhaps the Perpetualness is undetectable by normal science or it manifests after a person's first death (much like in Highlander or the Planeswalker spark of Magic: The Gathering). Another option is that he might be Ollanius Pius or John Grammaticus, who were tired of dicking around for another 10.000 years and wanted a shot at becoming a Space Marine. And an even better question is how the fuck the Eldar were able to recognize him for what he was after only a short period of interaction with them.
Cyrene Valantion
Cyrene Valantion was a common woman from Monarchia, a planet conquered by Word Bearers during the Great Crusade, until some fagots blew her home city to ashes to send a "Stop Worshiping Me!" message from the Big E to Lorgar. Since the smurfs weren't complete assholes they evacuated all civilians. Well, except Cyrene. She decided to stay out of the city borders and watch as orbital bombardment erased her home. Apparently watching an entire city being nuked was not her best decision, since she lost her eyes and almost died due to extreme light radiation burns. When the Word Bearers arrived they rescued her and figured that she was the only witness of their punishment, which turned her into some kind of saint in their eyes, so they offered her a position of Confessor/Holy Relic, aka "The Blessed Lady" in their fleet. During a few decades of her service she became on a short hand with captain Argel Tal and guided him to his path of the first Possessed Marine and overall awesome guy who kill loyalists and doesn't afraid anything. Well until muh Heresy, muh Drop Site Massacre and she get herself killed by some Custodes assholes for just being on their way. Needless to say Argel Tal cried a manly tears of rage over her corpse and swore revenge at Custodes, which he delivered just a few hours later butchering them all on the ashes of Istvaan V. Fast forward one year Erebus being a dick he was resurrected her to oil his machinations with Argel Tal. Mind you she was dead for a year and her soul was torn apart and eaten by multiple daemons whom Erebus "persuaded" to give the pieces back. Being a badass she was Cyrene recovered from the shock of being mutilated and tormented in hell surprisingly fast, until muh battle for Nuceria, her ship get blown up and she get rescued by none other than Damon Prytanis who told her that being resurrected turned her into Perpetual. And then... Clifhanger...
Alivia Sureka
Another female perpetual and empathic psyker and the most recent to be introduced. Unlike most of the others though she has no apparent connection to the Cabal at all, and in fact is much more closely linked to the Emperor. She had travelled with Him and undisclosed "others" to the planet Moloch where the Emperor somehow travelled directly into the Warp and stole portions of the Chaos God's powers.
She was left behind on Molech to guard the gateway to stop anyone else from passing through and doing the same thing. Which apparently she did dutifully for a few thousand years... meaning that she is the only other Perpetual in the Emperor's peer group who is actually loyal to him. (not counting Vulkan who didn't know and Thawn who came later)
When the Great Crusade arrived on the planet, the Emperor fortified the shit out of it, leaving detachments of Blood Angels, Ultramarines, Imperial Knights, Titans and Imperial Army, making her somewhat redundant so she settled down and married.
At least until Horus arrived during the Heresy and laid waste to most of the Imperial forces in a bid to follow in his father's footsteps and take the same power for himself.
Humorously, Alivia has several affectations brought over from the second millenium; she has a tendency to use use "modern-day" phrases such as "OK", which do not actually exist in the 41st millenium. She also carries around a book of Hans Christian-Andersen stories (probably one of the most priceless artifacts in the Imperium, if anyone knew what it was) which she reads to her adopted children.