A great example is a scene from the 1986 classic comedy film Withnail and I. Richard Griffiths plays Uncle Monty, an aging actor with an unrequieted crush on his nephew's friend. The friend, 'I' from the title, is terrified by this determinedly romantic homosexual and pleads with Uncle Monty to leave him alone. Monty refuses, following the younger man from room to room that night, finally stating: 'I mean to have you, boy, even if it must be burglary.'
He's talking about rape, of course, this is rape humour in one of the most beloved cult films of British cinema. The scene is hilarious precisely because it is so ludicrous: the obese Monty mumbling homoerotic prose as he stalks his horrified but pleadingly polite intended victim. The young man only survives the night by convincing Monty that he is in a loving homosexual relationship already with the nephew, even though both are actually straight. It is nuts, and sheer brilliance.
Rather less restrained is the Irish comedy Ireland's Savage Eye with this mad clip, featuring two Catholic priests managing to grab a child from his father and run away down the street with him. That's a joke about child rape by Catholic clergy, about as serious an issue as has been discussed in modern Ireland. Then the US has Family Guy, which features one offensive gag after another. In one episode the baby Stewie becomes sexually aroused by being spanked by his mother, even daydreaming about her dressed as a dominatrix while torturing him. Family Guy also features Herbert, a very elderly paedophile who walks with the aid of a zimmerframe while attempting to prey on the town's children. Or there is the hypersexual Quagmire, who in one episode asks to be left with the corpse of his wife for a few minutes of necrophilia. This stuff is on BBC Three most nights; I can only guess that a great number of people don't see it that they can still be sensitive enough to get mad about much more innocent comedy.
For example the cartoonist Gary Larson features a number of the complaints he received from readers in The PreHistory of The Far Side: A 10th Anniversary Exhibit, like the fury that greeted one (excellent) cartoon that showed a woman encouraging her dog to race into the dog flap of a door, which she has nailed shut: 'Here, Fifi! C'mon! ...Faster, Fifi!'
Larson had the patience to write out an explanation for why he thought the scene was funny:
First of all, the key element in any attempt at humour is conflict. Our brain is suddenly jolted into trying to accept something that is unacceptable. The punch line of a joke is the part that conflicts with the first part, thereby surprising us and throwing our synapses into some kind of fire drill....
But in this cartoon there's an immediate conflict; the reader is asked to accept the unacceptable - that the dog's own master (the standard, heavy-set, matriarchal-type woman) is setting up her own dog for an unpleasant experience....
So, what you see in this cartoon, I believe, is the classic conflict of one or more elements within a specific context, causing a momentary sense of confusion in the crebral contex and ultimately evoking some kind of response.
When I was a child I saw this idea inform some of the humour of Warner Brothers' Animaniacs, particularly the Slappy Squirrel character whose comedy consisted almost entirely of hitting rivals with cartoon explosives and anvils. In at least one episode Slappy shows disdain for modern environmental cartoons that don't involve hitting people with anvils and instead preach soppy moral messages!
Larson gives other astonishing controversies stirred up by his work, like that over one cartoon showing two dogs play thetherball with a tied-up cat. Larson is playing on the traditional cat-dog animosity that we also see in Tom & Jerry, rendering it particularly absurd as one of the dogs has a tongue sticking out of his mouth with concentration. It's silly and fun. The readers' responses were not:
No doubt some stupid mixed-up weirdo will see the cartoon and get some poor cat and try to emulate the cartoon... I am really offended by this cartoon. - Reader, Texas
As an animal lover I find the suggestion of a cat hung by the neck for the purpose of sport, regardless of the context, to be extremely offensive. - Reader, Northwest Territory, Canada