The DCU gives us the Allen/West/Thawne family — the first two branches of which have a millennia-old feud with the third, at least partly because of how crazily related everyone is. The highlights:
Inertia, genetically engineered from Bart Allen, also has some of Bart's grandfather's DNA. This grandfather was descended from the Evil Twin of Bart's other grandfather. This makes Inertia possibly the most inbred character in the DCU.
Captain Boomerang, Jr. turned out to be Bart's half-brother with a parent from the future.
Boomer, who's aged normally into his early twenties, might actually be younger than Bart's little brother. Blame time travel.
Superman has this happen both in his past (the House of El, whose history is detailed in The Krypton Chronicles) and in several alternate futures. You have the Superman Dynasty, various clones and half-clones, an adopted son who is the child of General Zod, a half-human son with Lois Lane, Superman's cousin Supergirl who was Ret-Gone and then brought back, Power Girl, who is Supergirl from a different universe, another Power Girl who's the Supergirl of a different universe to the other one, the Goo-Goo-Godlike Ariella Kent, the child of an alternate Superman and one of the other Supergirls (so not the cousin), Superboy-Prime (a teenage Superman from "our" Earth gone bad), Ultraman, Overman, any number of other Alternate Universe Supermen — the list goes on. Two alternate versions of Superman (from Earth-Two/the 1930s version and from Earth-22/the Kingdom Come universe) stopped by the main DCU in the 2000s; one of them died and came back as a Black Lantern.
Hawkman suffers so much from Continuity Snarl that most writers just gave up trying to sort it out; as expected, he's got a badly tangled family tree, not so much due to time travel but rather lots of reincarnation. The short version:
Prince Khufu of Egypt and his wife Chay-Ara are continually reincarnated. They become several familiar couples, including Brian Kent (himself a possible ancestor of Jonathan Kent) and Lady Penbrook, and Nighthawk and Cinnamon. In the 1940s, they become Carter Hall and Shiera Saunders, who become the Golden Age Hawkman and Hawkgirl. They get married and have a son, Hector, who grows up to be the Silver Scarab.
Hector marries Lyta Trevor, a.k.a. the Fury, daughter of the Golden Age Fury and adopted daughter of Miss America (itself a Retcon; Pre-Crisis Lyta was the daughter of the Golden AgeWonder Woman). Then he dies and ends up in The Dreaming, taking on the legacy of Garret "The Sandman" Sanford. He takes Lyta there to live with him, but when the Lord of that realm returns, he's banished to the afterlife and Lyta is sent back to Earth. Lyta then has a son, Daniel.
Daniel, meanwhile, goes on to become the new Dream, which makes him in some sense a sibling to the rest of the Endless. This also makes him Superman's spiritual uncle.
Shiera's cousin, Speed, has a granddaughter, Kendra, who tries to kill herself because of a Post-CrisisContinuity Snarl that led to at least three different Hawkmen existing in the same continuity. Shiera, without realizing it, takes over her body as a walk-in spirit and eventually becomes the new Hawkgirl in Justice Society of America. Meanwhile, Hector is reincarnated as the son of Dawn "Dove" Grainger and Hank "Hawk" Hall (no relation to any of the other Hawkmen running around), but he still thinks of Carter Hall as his father. Dawn's sister, Holly, became the new Hawk.
Oh, and Charley Parker/Ch'al Andar, the Hawkman sidekick Golden Eagle, is Shayera Thal's nephew since his father (Fel Andar) is Shayera's cousin.
The Bat-Family is a mild version of this (well, relative to other comics):
Bruce Wayne has four adopted children: his adopted sons DickGrayson, Jason Todd, and Tim Drake (the first three Robins), and his adopted daughter Cassandra Cain (the third Batgirl). Cassandra's biological parents are David Cain and Lady Shiva, two of the world's most infamous assassins and Bruce's former teachers. There's also Jarro, a clone of Starro the Conqueror who considers Bruce his father.
Bruce also has a number of biological children. His son Damian Wayne, the fifth Robin, is the child of Talia al Ghul, daughter of one of Batman's greatest enemies, Ra's al Ghul. It's also revealed that Bruce has two further biological sons, Terry and Matt McGinnis, thanks to genetic manipulation and a surrogate father. In Earth-2 continuity, he has a biological daughter, Helena Wayne (a.k.a. the Huntress), the daughter of Selina Kyle. The New 52Continuity Reboot left her stranded on the main DC Earth for a while while the DC Infinite FrontierSoft Reboot changes continuity so that she's now a Kid from the Future who became a Paradox Person after changing the timeline. The fact that the world thinks that her and Bruce are cousins instead of father and daughter only complicates matters further.
In the Kingdom Cometimeline, Damian's counterpart Ibn al Xu'ffasch is romantically involved with Nightstar, who is herself the daughter of Dick Grayson and Starfire (which basically means she's dating her adoptive uncle).
Not to be outdone, The Joker claimed in one story that he was the son of Batman's confidante and adoptive mother figure, Dr. Leslie Thompkins. But the Joker's got an incredible Multiple-Choice Past, so he's probably just making it up — but we can't be sure. And one issue of Anarky revealed that the title character was the Joker's son; this was originally planned to be just the Joker playing mind games with Anarky, but the series was cancelled before they could get there.
And then there's the Kanes. Start with the five siblings: Nathan, Philip, Martha, Jacob, and Unknown. Nathan married a woman named Katherine Webb (Kathy Kane) who became the first Bat-Woman after his death and was secretly a Spyral agent. She was the artificial daughter of Otto Netz, the founder of Spyral and had a clone-sister named Elizabeth Netz. Philip didn't marry or have kids as far as is known. Martha married Thomas Wayne, see above. Jacob married a woman named Gabrielle and was the father of Katherine "Kate" Kane, the second Batwoman, and her twin sister Elizabeth, the criminal Red Alice, which is why Kate is Bruce Wayne's cousin. After Gabi's death, he married Catherine Hamilton, because there aren't enough versions of that name in the whole mess. And the unknown son is the father of another Elizabeth: Bette Kane who was the original Batgirl (or Bat-Girl as is written Pre-Crisis) who later grew up to be the Titans West leader under the name Flamebird.
Damian's genetically engineered half-brother Respawn is the biological son of longtime Teen Titans villain Slade "Deathstroke" Wilson. Slade's daughter Rose is sometimes written as having a romantic relationship with Jason Todd, and has previously expressed interest in Tim Drake as well, tangling the tree even further.
Swamp Thing's supporting character Tefe Holland is the daughter of Swamp Thing and Abby Arcane Holland. Tefe was originally a floating spirit called Sprout, who tried to find a body from a recently deceased person, was eventually given a body through Abby Holland's fetus, which was conceived through the Swamp Thing possessing John Constantine and having sex with her. Due to Constantine having the demon Nergal's blood in his veins at this time, Tefe is also part demon. She eventually became an Earth elemental like her father, beginning a line of human Earth elementals as a new Swamp Thing in Swamp Thing vol. 3, having all of her father's powers but retaining a human appearance.
The Harper Family:
James "Jim" Harper (Guardian I) has been cloned a number of times and had his DNA used to create experimental subjects which makes his family tree confusing, and his guardianship/adoption of the original Newsboy Legion adds both the originals and their many clones to the mess. His most prominent clone has adopted his own Opposite-Sex Clone as well as Jim I's grand-niece Bobby. Jim had three siblings, all of whom have descendants mixed in with the superhero crowd in the modern age including the aforementioned Bobby.
His grand-nephew Roy Harper (Speedy/Red Arrow/Arsenal) had/will have a daughter named Lian with the super-villain Cheshire and was adopted by Oliver Queen tying him to that family. He started out as Jim I's nephew but is now his grand-nephew due to a sliding timescale that required another generation be added in to the mix. Roy is also known to be descended from Vandal Savage, tying him to another large dysfunctional family.
Jamie Harper is pregnant with Mon-El/Lar Gand's child, meaning that even without the Cadmus experiments their family was going to end up with some extraterrestrial DNA. She is Jim I's other grandniece, and spent time as a GCPD officer and the police contact for Tim Drake before moving to Metropolis.
Wonder Woman originally played fast and loose with mythology, with the Olympians that appeared being played more like powerful aliens that some people might worship. Later iterations imported the mess of the original mythological family ties of the Olympians from Classical Mythology and added to it:
Golden Age Diana was the daughter of Hippolyte and, depending on one's reading, Aphrodite as while Di only calls Hippolyte mom both women call Diana daughter and were the two who together brought about her birth. Aphrodite does not seem to be related to the other iterations of Olympians who appear in this continuity, but her relationship with Mars retains romantic overtones despite the fact that they've been fighting for thousands of years.
Post-Crisis on Hippolyta is confirmed to be Ares' daughter as in mythology, making Diana Ares' granddaughter, and Zeus' great-granddaughter. This means that Diana is the grand-niece of the much younger Cassie Sandsmark, illegitimate daughter of Zeus, who is Diana's sidekick as Wonder Girl. Diana's family ties to the Olympians get brought up very rarely, with Ares only pointing it out when she asks why he's gone out of his way to save her life, but Cassie has these ties thrown in her face constantly and doesn't appreciate it. The Olympians have a habit of addressing each other by relationship; for instance, Zeus calling Hera his sister-wife, which highlights the mess of their incestuous family tree.
The New 52 further complicated matters by revealing Diana was Zeus's daughter rather than the daughter of Hippolyta and Aphrodite/five goddesses as she had been in previous iterations. Cassie was eventually revealed to be the daughter of one of Zeus' other illegitimate children. This was all retconned to have been false implanted memories by Wonder Woman (Rebirth) until Robinson treated Zeus as Diana's father and muddled the continuity. Rebirth is also the first mainstream DC continuity to treat Aphrodite as Zeus' daughter.
