"Dark Grepher" in the artwork of "Darklight".
The Dark counterparts are a series of DARK monsters that is identified by an existing non-DARK counterpart and 「ダーク」 in their Japanese name. Dark counterparts also have a twisted, sinister appearance compared to their original forms, which can be especially striking if the original form was that of a benevolent monster. All Dark counterparts share the same ATK, DEF and Level with their non-DARK counterpart.
Dark counterparts were first released in the OCG and TCG in Phantom Darkness, but dated back to the anime with "Rainbow Dark Dragon". The TCG exclusive Dark counterpart monsters were introduced in OCG in the Extra Pack.
Dark counterparts usually have effects similar to their counterparts (with the exceptions of "Dark Grepher" and "Dark Valkyria", whose counterparts are Normal Monsters), but reworked to go with the theme of manipulating DARK monsters you own or control, typically either Summoning them, sending them to the Graveyard, or banishing them (from the Graveyard) to trigger effects.
Although they do not explicitly support Dark counterparts, several cards released in Phantom Darkness work very well with them. "Doomsday Horror" gains power from banished DARK monsters and can "reload" your Graveyard with the banished DARK monsters. "Escape from the Dark Dimension" can Special Summon one of the banished DARK monsters, and "Allure of Darkness" increases your draw power while banishing another DARK monster. "Veil of Darkness" can also vastly increase a DARK-user's draw power while flooding the Graveyard with DARK monsters to use as a resource.
Individual Dark counterparts splash well into a number of other established archetypes as support cards. They work best with Archetypes that focus on Graveyard control and which are composed of DARK monsters, such as "Destiny HERO" monsters, Zombies, and Fiends.
"Adreus, Keeper of Armageddon" is seen as the Dark counterpart of "Tiras, Keeper of Genesis", both cards sharing rank, ATK, DEF and having a similar name. However not having "Dark" in its name and being of a different type ("Adreus" being a Fiend and "Tiras" a Fairy) result in "Adreus" not being placed in the series.
"Shadowpriestess of Ohm" is occasionally placed within this series, since she is a DARK monster with an effect related to other DARK monsters and bears a strong resemblance to another existing card ("Lady of Faith" and "Elemental Mistress Doriado"), as well as having been released in Phantom Darkness alongside many of the Dark counterparts. However they possess differences in ATK and level, and as a result, she is not a Dark counterpart.
"Darkflare Dragon" is often considered a Dark counterpart to "Lightpulsar Dragon", since it is a DARK monster and has "Dark" in its name. However they possess differences in ATK, DEF and level, and as a result, it is not a Dark counterpart. Also, judging from the story of Dragons Collide in the official site, "Darkflare Dragon" is more of a companion or comrade to "Lightpulsar Dragon", than a counterpart.
"Dark Elf" almost fits, as well, as it is obviously a Dark counterpart to "Mystical Elf" with practically the same design. The key difference is that the ATK and DEF of "Dark Elf" are inverted from "Mystical Elf".
Trap cards that may fit are "Dark Mirror Force" and "Darkfall". For the former, the effect is somewhat reversed from the original and with the latter the effect is just watered down. However, the effect has nothing to do with DARK monsters.
Archetypes composed of DARK monsters based on previous monsters, like "Malefic" or "lswarm", are not considered part of the series because they lack the attributes that compose it (like sharing the ATK, DEF and Level with their non-DARK counterpart, or having "Dark" in their name). Instead those archetypes' attributes and appearance transform their members into different versions of the original card, like Corrupted versions ("Malefic") or infected versions ("lswarm").
In Yu-Gi-Oh! ZEXAL, the ZEXAL power allows the user to create "Zexal Weapon" cards, while its dark counterpart, Dark ZEXAL allows the user to create "Dark Zexal Weapon" cards, though only one was observed when the power was used.
The "Lightray" Series can be thought of as the inverse of Dark Counterparts, as they represent LIGHT versions of existing monsters that exhibit synergy. "Warrior Dai Grepher" has both a DARK counterpart and a "Lightray" counterpart.