Asexuality: To a downright supernatural degree. He's immune to the effects of SCPs that affect sexual desire. Also, normal women tend to find him repulsive or unnerving, at an almost instinctual level.
Humorously, after D-Class personnel tried to use the Gay Bomb on him, he compares himself to The Sisters of The Shawshank Redemption, and will pull it on anyone else who tries to repeat the stunt.
Heroic Comedic Sociopath: Known to pull pranks causing death or serious injury to others on a whim, shoot at people for no apparent reason, and otherwise engage in violence when bored. Also drove one of his assistants to a psychotic break.
At least, that was what Dr. Clef thought his motives were. It turns out that Kondraki's original motive was actually just stopping Clef from causing more chaos for the foundation. At most, Kondraki was psychically manipulated by 239 without realizing it, as he discusses in an after-action interview log with an overseer.
Dogged Nice Guy / Stalker with a Crush - Requiring Agent Diogenes to do psychological evaluations once a week instead of the normal once a month, so he can muster the courage and try to ask her/him out.
Modern Major General: He's assigned to paperwork despite having contained several SCPs and being an explosives expert. Granted, he's good at paperwork too...
Badass Boast: Captain Dmitri Arkadeyevich Strelnikov, Twice Winner of Order of Suvorov for Exceptional Leadership Under Fire and Selfless Heroism and Bravery, One Who Has Saved Many Children From Burning Buildings.
Nice Character, Mean Actor: The opposite of Gears. Got himself banned for making inflammatory comments and requested all his work (most notably Wanderlust stories, the Black Queen and SCP-808) be taken down. It was.
No OSHA Compliance: Subverted. "Who here is willin' to die rather than give up on the mission? One, two, three, four… Okay, you five fail. Counter to what some dingbats will tell you, the latter is actually the preferred option."
More Dakka: "...that's when you pull out your gun and you shoot the fucker. If that don't work, you shoot it again, because ninety-nine times outta a hundred, shootin' will work if you do enough of it."
Eldritch Abomination: When brought in to terminate 682, SCP-343, who is thought to be God, refuses and remarks "He's not one of mine. Deal with him yourself." Hoo boy.
Exactly What It Says on the Tin: SCP-682 really is a Hard-To-Destroy-Reptile. Although the picture used in the article is of "The Moscow Monster", which was really just the corpse of a beluga whale.
Everything AliveThrough Alien Eyes: One possible explanation for why it always tries to kill everything except SCP-053. It's not evil, it's just that everything alive in our world except SCP-053 is so horribly, gut-wrenchingly disgusting and wrong that SCP-682 can't help reacting by trying to make us all stop existing ASAP. It also didn't try to kill Dr. Clef for some reason. It just stared at him. It's anyone's guess what this means.
Extreme Omnivore: It gains energy from anything it ingests, even the acid used to contain it.
Flowery Insults / Sesquipedalian Loquaciousness: It calls SCP-999 a "feculent little snot wad" and invites it to "[DATA EXPUNGED] and die", and generally gets pretty vicious verbally if it's restrained physically.
Godzilla Threshold: "Special Containment Procedures: SCP-682 must be destroyed as soon as possible."
Infernal Retaliation: The Foundation once attempted to launch SCP-682 into the sun with a very large cannon. It came back ON FIRE. Of course, this was only mentioned in the joke SCP entry for said very large cannon, so it is not canon by virtue of the 1543-j not existing within SCP canon (nebulous and ill-defined as it is). Just cannon. It also had wings that launched razors-sharp feathers.
Inversion: SCP-1364: 682 is an unidentifiable "reptile" that adapts to survive and hates everything while 1364 is an anteater that, despite being harmed by bright lights, still wants a hug.
Dr. Clef also doesn't seem to trigger its murder-death-kill reflex, whatever that means...
Pet the Dog: SCP-053 is possibly the only living thing that 682 didn't immediately try to kill - in fact, 053 played with it. Did we mention that this is the opposite of what usually happens, given that 053's main power seems to be to make people inexplicably and violently hate her after some time?
Went into Papa Wolf and Even Evil Has Loved Ones territory when 682 attacked the personnel sent to retrieve 053, presumably believing they'd harm 053.
That or it was just doing whatever it usually does, mauling anything in sight.
053's other power is that anyone or anything that causes her harm dies. It's possible that 682 could sense this power and was merely adapting as it always does.
Unstoppable Rage: It's not as popular as its other traits, but SCP-682 has episodes that are hard to describe as anything else, where it seems to lose control and become even more aggressive and even harder to incapacitate than usual. The abovementioned incident with the personnel trying to remove SCP-053 is a good example.
Arson, Murder, and Jaywalking: "SCP-076-2 has however, shown that it has great knowledge of human anatomy (although in a highly violent context), military tactics of open warfare, metallurgy, and, strangely enough, the care of livestock."
Ax Crazy: If Able is bored (which is often), he'll entertain himself by going on homicidal rampages.
Berserk Button: Presumably, exposure to a picture of the symbol on SCP-073's forehead. (SCP-073 is Cain.)
Beyond the Impossible: Able was once tasked (though as a separate incident/story, its canonical status is iffy) with trying to kill 682 listed above. They tore each other to ribbons but neither quite get the job done, took a break, went back into it, and fought so hard that they caused a [DATA EXPUNGED] event, implied to have been a hole they broke in the universe. Which means that one or the other's powers went off the scale, or that they're both such insane Human/Eldritch abominations that their co-presence messed up the laws of physics.
Cain and Abel: He's the Abel. Notably, 6,000 years of undeath has reversed his role; he's now more of a Cain than Cain himself (who is also an SCP; see below).
Canon Sue: Invoked. Able is explicitly the most sue-ish you can go, and you are not allowed to add an SCP more sue-ish than him. It's called the "Able line".
Retcon: Recently, the main 076 article was rewritten to remove the Mobile Task Force Omega-7 stuff, and make Able less "lolawesome". He's less of a Wolverine expy now and more of a humanoid bundle of murder. He is also now completely hostile towards the Foundation; no longer is he working for any side.
The Mobile Task Force Omega-7 stuff was later worked back in with key changes. The "official SCP-076 file" makes it VERY clear that he's Chaotic Neutralat best, while the records of his time in Mobile Task Force Omega-7 state that the instant Able got bored again, he reverted back to slaughtering SCP personnel.
Spell My Name with an S: Proper spelling, as listed on the main article and by Word Of God, is Able. Too many people misspell it using the Biblical spelling, though.
Worthy Opponent: SCP-076-2 lamented the loss of an SCP agent who was able to match him in combat. Partly because said agent killed as collateral damage in an airstrike (to stop another SCP) instead of in combat (as 076-2 thought a Worthy Opponent deserved) and partly because fighting the Foundation was really boring without said agent there to make it challenging.
Deconstruction / Fridge Brilliance: Able has no interests beyond killing people, is perpetually bored, can summon weapons out of an apparently unlimited space and respawns upon death. He is a videogame player character.
Noodle Incident: What IS she carrying? What do they do to her?
"Further recruitment of Class D Personnel is to take place among convicted sex offenders only, to minimize possibility of a second botched 110." Read this. A better (and more horrifying) question is: what don't they do to her?
The writer apparently once claimed it wasn't the obvious. Allegedly, it's something worse.
Berserk Button: Being called a kitsune. "Personnel asking what the difference is are to be reminded of the difference between a Cherokee Indian and a New Delhi Indian". Furries also seem to really piss her off.
The Fair Folk: This is technically what a kumiho is, but her sheer malevolence makes the Court Unseelie look perfectly benign by comparison, and that's saying a LOT.
The Trickster: in-between eating humans, she loves to play sick tricks on them, seemingly purely For the Evulz. She tricks a mother into eating her own child. Also, when a team of agents arrives to apprehend her, she mentally dominates them and feeds them meat with rice... only the meat turns out to be rotting human flesh, and the rice is live maggots.
The Vamp: She seemingly exploited this to bite off an agent's genitals, before showing it to him and proceeding to tear out his liver.
Yamato Nadeshiko: can pretend to be one in order to increase her mental hold over her victims.
Eloquent In My Native Tongue: Doesn't have a "native tongue", per se, but it's apparent that she has complex thoughts and is frustrated by her inability to express them well.
A Wizard Did It: Not even Deeds himself is quite sure how he's able to do what he does. Thinking about it too much seems to distress him.
Battle Butler: Well, Deeds is a butler... and you can send him to kill people.
Death Is a Slap on the Wrist: Whenever Deeds is killed, no matter how severe his injuries, he comes right back once his corpse is out of sight and the bell is rung.
Offscreen Teleportation: He needs to be unobserved to bring back items, and knows if he is being observed. If there are cameras, they simply malfunction for a minute or two, with Deeds not knowing or caring how he got the item.
Blatant Lies: An earlier description was an over-the-top cover story that Yetis are hugely dangerous beings with "death auras"; the current one is a "regular" cryptozoology description.
Humans Are Bastards: "Then their civilization fell. And we did it. By 'we' I don't mean the Foundation. By 'we', I mean humanity."
Laser-Guided Amnesia: "We left no traces. Not even our own memory. We turned one of the ["yetis'"] weapons on ourselves, wiped out any knowledge of SCP-1000 and the greatest civilization the planet had ever seen."
Not so Different: "SCP-1000 are just like us. That's what makes them so dangerous. We wiped them from history and memory. We dissolved their civilization and we slaughtered most of their species. Just ask yourselves: If they got the chance, what more would they do to us?"
Fortunately they forgive us, as long as we let them "back in". Unfortunately their forgiveness depends on how soon we allow them "back".
Names to Run Away From Really Fast: The other organizations might've made up their ominous names, but the name of this group would imply that they actually have a partner named Dark, of all things.
ALL UPPERCASE LETTERS: Just like ancient Rome, that universe apparently has no lowercase letters.
Alternate History: It exists in a world where the Roman Empire has endured to the present day.
For Want of a Nail: SCP-961 implies that the only reason our world hasn't ended up the same way as theirs is because of a mysterious... someone influencing historical events.