Red-sided garter snakes famously engage in what can only be described as orgies, forming large "mating balls" of writhing snakes.
Toads mate in a position called amplexus, in which the male mounts the female from behind and fertilises her eggs externally.
If competition is intense, several toads may mount the same female, a situation called "multiple amplexus". This can result in the female being drowned, but assuming she survives, it can also result in her producing offspring by several fathers. Media reports of a frog with three heads may also have been an instance of multiple amplexus.
Promiscuous sex can also be a form of social bonding. This is most famously observed in bonobos, a kind of chimpanzee. Members of a bonobo troupe have sex with each other in pretty much every combination, and engage in a host of different sexual activities. Their societies are female-dominated and seem to be almost entirely non-violent.