In the original comics, Firestorm was an amalgam of slacker student Ronnie Raymond and physicist Martin Stein, then Raymond and Mikhail Arkadin, then Raymond on his own. After his death, the new Firestorm was teenager Jason Rusch, who would combine with whomever happened to be nearby but would eventually combine with his friend Mick Wong, then Stein, then Firehawk, then his girlfriend Gehenna. The animated version was formed by a combination of gym teacher Ronnie Raymond and his student, a pre-teen Jason Rusch (now a science whizz-kid to provide Stein's atomic knowledge). Unusually this switches their positions, as normally Ronnie was the physical body of Firestorm and Martin was the voice in his head, now, Jason is the intended physical body though with a lot of added musculature, and Ronnie speaks in his head, switching the muscle and brains around. As of Brightest Day and the New 52, the Rusch/Raymond combo has appeared in the comics as well.
In the comics, the Golden AgeCheetah was Priscilla Rich, a wealthy American socialite who had no powers and wore a cheetah costume, while the post-Crisis Cheetah was Barbara Anne Minerva, a British archaeologist who was turned into a superhuman cheetah creature by the plant god Urzkartaga. The TB&TB version of Cheetah is Priscilla Rich, but like her successor, possesses superhuman abilities that were given to her by Urzkartaga.
The TB&TB incarnation of Damian Wayne combines elements of three separate children of Bruce Wayne from different continuities - obviously he gets his name from Batman (Grant Morrison), but the story he appears in is more like the Golden Age "Imaginary Stories" with Bruce Wayne Jr. (complete with the Framing Story of Alfred writing fiction). And his mother isn't Talia, like comics Damian, or Kathy Kane, like Bruce Jr., but Catwoman like Helena Wayne of Earth-2, who became a vigilante in order to avenge the death of her mother, and continued on, taking her father's place after his subsequent death, in this case, both Batman and Catwoman die at once due to Joker's protege Joker Jr. rather than dying individually.
The Weeper in "Joker: The Vile and the Villainous" is based on a Golden Age character who was a foe of Bulletman, but the story itself is based on a team-up between Joker and a character called Willy the Weeper. The composite character has the original Weeper's real name and appearance (and is shown fighting Bulletman in flashback), but like Willy is an Ineffectual Sympathetic Villain who cries genuine tears for his victims, with his team-up with the Joker intending to cure him of his habit of crying about the people who will be harmed by his crimes.
Krull the Eternal is mostly Vandal Savage, but his name and appearance come from Captain Marvel's caveman enemy, King Kull. He also takes visual cues and a voice actor from Darkseid's son Kalibak.
The Hunter's name and appearance come from the Faceless Hunters who appeared in Strange Adventures. His role as humanoid frontman for Starro is loosely based on Cobi from R.E.B.E.L.S.
Equinox is two Justice League of America villains: Libra (balance-obsessed, cosmic-powered villain) and the Gray Man (embittered and crazy ex-agent of the Lords of Order).
OMAC enemy General Kafka is combined with the completely unrelated character Shrapnel, for no reason that's easy to figure out.
The Batman of Zur-En-Arrh is an existing character in his own right, but his civilian identity (largely unexplored in the comics, but heavily expanded on in the show) is heavily inspired by Clark Kent. Likewise, Vilsi Vayla is a combination of Vicki Vale (name and appearance) and Lois Lane (personality, voiceactress, and relationship with the two Batmen).
In early episodes, Mongul and his sister Mongal often took over roles more associated with Darkseid and his lieutenants, like commanding the Female Furies and Steppenwolf. The show generally stopped doing this after Darkseid was properly introduced about halfway through Season 2.
The Reverse Flash is Eobard Thawne, but he has Hunter Zolomon's red and black eyes.
Jarvis Kord, Ted Kord's Evil Uncle, takes Max Lord's role as Ted's killer. He's even voiced by Tim Matheson, who voiced Lord in Justice League Unlimited.
The version of Phantom Lady who appears in "Cry Freedom Fighters" combines elements of three characters who have used the name. She has the origin and costume (well, a more modest version of it) of Sandra Knight, the original Phantom Lady. She uses holographic technology just like Dee Tyler, the second Phantom Lady. And finally her use of invisibility and intangibility technology are borrowed from the third Phantom Lady, Stormy Knight.
The series' interpretation of the Red Hood is a combination of the original Red Hood (who was established in some continuities to be an identity used by the Joker before the fateful day he fell into a vat of chemicals and became the Harlequin of Hate we know him as) and the Jokester (the Joker's heroic counterpart from the Crime Syndicate's universe).
