When you think about reproduction (or mating, or the act of copulation that spawns new individuals of a species) you think about two constituents of the same species of different sexes coming close for some time . One individual is a male and the other is a female, both are equiped with specialized reproduction organs.
Well... there are some species that lack external reproduction organs in one of the sexes. Also there are species that really don't like touching each other...
Our first case of weird mating habits comes from the ocean, the deep ocean. The deep sea squid is cannibalistic, that means they eat each other. That's one impediment, the other impediment is that the male is quite small compared to the female.
So how does a species that practices cannibalism that has small males compared to females reproduce ?
The male has dart like spermatophores that it shoots at the females. Exactly, the male comes close enough and shoots sperm filled darts at the female. The female is receptive to sperm all over her body. The species is called "Moroteuthis ingens".
Other species of squids just have the male wound the female with its beak.
The next weird are bed bugs. The female has no external sexual organs, so the male has to cut an opening into the female to delivers his genetic cargo.
The male has a penis that can cut into the females exoskeleton. The funny thing is that both males and females in some species of Cimicidae have the bladed phallus. So bloody fights ensue between horny males and not so horny females.
That's traumatic sex ...