Lore
The "Dark Servants" (a term found in various in-game descriptions) are a heterogenous ensemble of entities spawned by the Abyss itself, creatures corrupted by it or beings that are bent to extinguish the First Flame in its name. A trait shared by this group is the weakness - and sometimes fear - for the energy of Fire and the essence of the Gods: this weakness is the same as the Undead's because they too are linked to the Abyss, not physically but through the Dark Soul itself, while the Gods are born from the First Flame. Non-human entities like lesser monsters and Gods can be corrupted by exposure to the Abyss, but their body will not be radically altered, while human beings, possessing a shard (aptly called Humanity) of the Dark Soul, instead will become horribly warped. Subjects of a rogue Humanity degrade into beast-like monsters, usually developing some sort of feeding maw in unusual places, multiple glowing red eyes and abilities centered around the Dark element and the draining of the enemies' souls. The most powerful Dark beings have a unique gift: the power to traverse the Abyss to reach different points of space (like the Primordial Serpents and the Dancer of the Boreal Valley) or even to go back through time itself (like Manus did with his giant arm).
Manus,the first Dark Servant
Plot
Dark Souls
The lost city of Oolacile is the nest of the Bloatheads, the first example of living humans touched by the Abyss. A similar but even more atrocious transformation is what happened to Manus, twisted into an eldritch and misshapen behemoth that did not even resemble a human being, anymore. A similar fate happened to the Four Kings (once proud monarchs, reduced to soulless shells) and to Artorias, one of the Four Knights of Gwyn: belonging to the race of the Gods saved his physical form but still the Abyss shattered his mind and corrupted his body, which continuously seeped a purple ooze (the "corrosive darkness of the Abyss") that tainted his sword. The Darkwraiths are somewhat of a separate group because they are Undead who willingly pledged their loyality to Darkstalker Kaathe, one of the most ancient emissaries of the Abyss: they are literally the crusaders of the Abyss, armed with weapons made to harm the Gods and to steal Humanity. Aside from the Primordial Serpents, the most ancient denizens of the Abyss are the Humanity Phantoms, disembodied and barely sentient shards of the Dark Soul.
A champion of the Abyss
Dark Souls II
The Dark Stalkers not only had a body similar to that of a Bloathead but also a high elemental resistance to Dark and an absolute fear for fire. The Darklurker has an almost pristine body, altered but not misshapen, so it was potentially a member of the God kin. It is unknown if the Sanctum Priestesses are true Dark Servants since their transformations were initiated by Sinh's venom, but regardless, their ability to manipulate Dark through hexes and their headgear - similar to the horns of Manus - are unsettling.
Dark Souls III
The last known cycle is plagued by Abyssal activity well beyond the past times. The first and most evident sign of this outburst was the appearance of Pus of Man, entities that merged the worst part of a Primordial Serpent and a rogue humanity. They force themselves out of a dead body like a churning tumor of black fluid, thus taking a serpentine form (a wide triangular mouth atop of a long neck) with some twisted draconic features (a skeletal, clawed limb and long horns jutting out from their liquid body); this "imperfect dragon" appearance and the fact that they emerge only from Undead and Ancient Wyverns confirm a relation with the Primordial Serpents, abyssal dwellers who envied the Dragons and allied themselves with the first Dark Lord. Pus of Man are weak to Fire to the point of twitching and shrieking in pain at the hit of a plain torch, but should not be underestimated; they are resilient creatures with enormous physical strength, and sometimes, they can spit a Curse-inflicting fluid.
Far from the land usually inhabited by Humans, Lord Aldrich and his servants kept dreaming of a world without Flame, drowned into a liquid darkness called "the Deep". Aldrich's ability to slay Gods seems an echo of the ancient occult weapons, but he became an amorphous horror well before his communion with the Deep (before his forced entombment, he developed an insane craving for the flesh of the sentient). Aldrich's vizier, Pontiff Sulyvahn, was probably the only member of the God's race (his branch-like wings are typical of the Abyssal Undeads but he is way too tall to have been a human) to align himself with the Abyss. Aside from new eldritch powers, Sulyvahn's preserved free will also made him able to manipulate the Profaned Flame, a name that describe perfectly a true source of Fire that can be wielded by a Dark Servant.
His knights are hollows (probably once God kin since they are too tall to be Undeads) but their "eaten away by insects" weapons and their Dark spit attack reveal a connection to the Abyss. Aldrich's cult was responsible for the creation of various kind of twisted Dark Servants, starting from the Sewer Centipedes (maybe they were once human slaves but became sea spider-like aberrations composed by humanoid arms around a gaping maw) and the Monstrosities of Sin (these Ogres suffered an ordeal that remade their heads into giant hands with a central maw - exactly like Manus' - and sprouted dozen of eyes on their stomach); Sulyvann too used cursed rings to created the Deep Accursed and the Beasts, powerful Irithyllian knights that became a hellish amalgams of man and primeval monster, much like Manus.
It is unknown how the Cult learned to mutate even the God kin or if this process still requires a rogue Humanity, but it is well possible that some ancient being helped them. A less fortunate case of Dark allegiance is that of High Lord Wolnir - he was once a mighty human king who tried to harness the power of the Abyss. Nevertheless, his plan backfired and the Darkness swallowed him; thus he became a skeletal giant, able to stave off his demise only thanks to his enchanted bracelets and the absorption of countless sacrificed souls.
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A Deep Accursed created by Sulyvahn
An interesting exception was Rosaria, denizen of the Cathedral of the Deep. Even if she was said to be a goddess, she had none of the usual attributes of the Gods' race (radiance, etc.), thus making her closer to Velka (another goddess whose existence was considered a threat to the Gods of Anor Londo). Her physical form was even more unsettling, not due to some horrible mutation but because she resembled Alsanna, one of Manus' "daughters." Even her soul was absolutely unique - it was not a bright star (like that of the Gods) nor a pulsing darkness (like that of Manus or Aldrich), but instead resembled a serpentine, red-white tendril of fire. The same Cathedral is infested by one of the few known native creatures of the Abyss. This is a species of insects that thrives in the Deep, pale worms that travel in swarms that can devour a creature alive or parasitize corpses in order to merge into almost humanoid, more powerful beings; the Man-Grubs are things "reborn" thanks to Rosaria's power, but it is not known if they were humans that wished to be remade into worm-like monsters or Corpse Grubs which consciously sought the goddess' intervention in order to lose their swarm form.
The Deep
Not much is known about the region of the Abyss called by this name. It is described as a once-sacred place, but it became a churning well of dark souls after many "abhorrent things" rotted there. Since Aldrich foresaw an "age of the deep sea" following the fading of the First Flame, creatures and places close to the Deep are vaguely reminiscent of deep sealife and are covered with calcified growth that resemble worms or pale corals.
Lord Aldrich, prophet of the Deep