Family Guy did an incest joke about Donnie and Marie. But nowadays they seem to favour implying repeated events of incest between Meg and Chris...
In "Halloween On Spooner Street" Meg goes to a Halloween party as a masked Slutty Cat and hooks up with a boy in an all-concealing Optimus Prime costume. After seven minutes in the closet, Connie D'Amico opens the door to find that Meg is making out with Chris, to the horror of all. Later though, Meg and Chris seem to warm up to the idea.
In "Save The Clam" Chris has to stand in for a corpse. When his suit starts itching Meg tells him to stop scratching his balls, and he asks her to do it for him. He enjoys it a little too much...
In a more recent episode, Meg asks Chris if he wants to "practice kissing again." Chris turns her down only because he's busy watching for the evil monkey on a security tape.
In the movie, Lois complains to Peter that, with Chris and Meg around, they have no privacy at all and asks if they shouldn't be dating by now. Of course Peter assumes she meant dating each other.
In "High School English" as Peter reads "Of Mice And Men", Meg plays Curley's wife, and Chris plays Lenny. Curley's wife attempts to seduce Lenny, but her euphemisms go right over his head and he snaps her neck.
In "Fresh Heir" Meg walks into Chris's room dressed only in a towel and tells him that their bath is ready - then realises Peter's the only one there.
In "Nanny Goats" the hired Russian nanny walks in on Chris and Meg playing 'Doctor' - by which, they are about to start kissing.
Transformers, Orion Pax and Ariel were originally boyfriend and girlfriend. After their bodies were destroyed, Alpha Trion recreated them both as Optimus Prime and Elita One and the two continued the relationship in their new lives. Their anatomy turned out to be so similar that Optimus is able to save Elita's life with an energy transfer, and Optimus seemed a bit taken aback when Alpha Trion told them about their origins. When she steps close to him at the end, he even walks away quickly. No one outright mentions the word "incest", but it's heavily implied that something weird's going on.
"Something weird is going on" is that Optimus had forgotten who his creator was so it's more surprise that he's learned Alpha is his deadbeat dad. Also Elita was leaning in for a kiss so it may be more "hero denying his pleasures" than anything else. Also two reasons he denied her: parents' anger at robots kissing and kids's reaction to seeing a parental (albiet fictional) figure smooching other than a quick peck on the cheek.
In South Park, there is an episode in which Stan has problems with his older sister, Shelly, who constantly beats him. When he asks his friends' help, Kenny suggests something through his orange parka. Although his words are muffled, the suggestion is obvious, because Stan replies, scandalized: "Sick dude, she's my sister!"
Kyle suggests that Stan use The Power of Love to stop her, just saying "Shelley, you're my sister and I love you..." the next time she tries to beat him; Kenny then finishes Kyle's sentence with "...and I want to take off your bra."
In American Dad, In the Episode "Stannie Get Your Gun" Roger tricks Steve into believing he's adopted. This triggers a bit of a Heroic BSOD in Steve and one of the first things he does is go to his sister Hayley, says there's always been "sexual tension" between them, then makes out with her. Hayley is understandably surprised and repulsed.
In the episode "Meter Made" Hayley poses nude for Roger for his painting. Steve masturbates to it. In his defense, he didn't know it was Hayley (the painting stops just above her lips) and when he finds out he's understandably Squicked out.
In the episode "An Apocalypse to Remember" The Smith's are invited to a party celebrating ethnic minorities in America. Unfortunately, due to Stan misreading the invitation, the family turn up wearing blackface make-up and the Smiths are forced to leave embarrassed and angry. At the car this dialog take place:
Steve: What a boob.
Stan: What was that, Steve?
Steve: Um, I, uh... asked Hayley if I could squeeze her boob.
Stan: I love it when you kids get along.
Cletus and Brandine from The Simpsons are related to each other in all sorts of ways. One of them being as brother and sister.
In the episode "Kill the Alligator and Run", the Simpson family flees from the authorities of the state of Florida. The family ends up working in a restaurant and they live in a trailer. So you get this scene:
Homer: Yep, this place is great, and someday when Lisa and Bart get married it will all be theirs.
Marge: You mean when they marry other people.
Homer: OK... but I'm not paying for two weddings.
Aversion: With the communal raising of children the titular species employs in Gargoyles, this was an early fan idea about Demona's and Goliath's relationship, until Word of God severely beat that out of the fandom by stating that the pheromones a gargoyle releases when he is courting smell horrible to any close family relation. This is only natural, really, since nature prefers genetic diversity over in-breeding.
Interestingly, gargoyles still consider the other gargoyles they were raised with to be their siblings, but coupling inside this social family appears to be perfectly normal simply because if they had already evolved a physical mechanism to prevent inbreeding (the pheremones), then there'd be no pressing advantage to evolving a psychological mechanism (Westermarck Effect—the origin of the incest taboo).
Jackal from "Gargoyles" is a Complete Monster who, along with his sister Hyena, is one of the most ridiculously Ax Crazy characters in the Disney canon. However, when Hyena falls in love with Humongous Mecha Coyote, he seems to find it a little more reprehensible than just a normal big brother would, especially considering it's nothing worse than what he's done, and comes off much more as a jealous Stalker with a Crush. He later got most of his body replaced with cyborg parts, and they end up in a pretty sick Love Triangle for most of the series.
While Jackal's disgust for Hyena's robophilia is fact, there's no actual evidence that his reasons for this are anything more than the normal reaction to discovering your sister likes to hump toasters. There's nothing in canon or Word of God to suggest there was a love triangle at all- especially since Coyote wasn't interested in Hyena, either.
The titular characters from The Twins of Destiny had this implied, through their interaction throughout the series but mostly their decision in the final episode to leave everyone else and everything they have bonds with behind to be together. Just for the record: Jules and Julie both have a different set of parents, but their mothers are implied to have been incarnations of the Moon Goddess. Their mothers died during the twins' birth and their fathers were taken prisoner by the Empress of China, who wanted the twins dead. Jules and Julie were smuggled out of the country and brought to France, where they were raised by one man as siblings until they were about 14 years old. They know they aren't biologically related, but they do consider themselves siblings, often referring to the other with "my brother" or "my sister".
'Subtle subtext'? Hell, Linda Ronstadt and James Ingram's music video for their cover of the song plays it as a straightforward romantic ballad...and they didn't have to change a word. It's still a lovely song, but...yeesh.
An episode of King of the Hill had Bill meet and fall in love with a beautiful single mother named Charlene. Dale, suspicious of her daughter, does a DNA test and discovers that she has the same paternal DNA as Joseph, which means they're both Chocolate Babies fathered by John Redcorn. When Hank tells Peggy, she freaks out because the two kids have been getting very close and sends Bobby off to play fifth wheel and prevent anything really Squicky from happening. In the end, the Hills convince Redcorn to seduce Charlene away from Bill, leading to her moving away.
An extremely disturbing scene in Avatar: The Last Airbender when Zuko goes to confront Azula for giving him the credit for killing the Avatar. Azula started acting all coy and seductive towards Zuko's questions(which, being Azula, was probably a way to creep Zuko out and distract him from his questions yet still managing to highlight his doubts and uncertainty).