Dogs
The domestic dog and the wolf are the same species, Canis lupus. DNA evidence has proved this beyond a shadow of a doubt. While there may well be occasional hybrids with coyotes (Canis latrans) where domestic dogs and coyotes occur in the same place, these hybrids aren't normally crossed back into the domestic dog gene pool, and the dogs kept as pets are "pure" wolf in terms of genes.
Cats
The origin of domestic cats has been argued over the years, but the DNA evidence implies they are descended from Felis silvestris lybica, an African variety of Felis silvestris, the wildcat. The domestic cat certainly does cross with other subspecies of Felis silvestris, including Felis silvestris silvestris, the Scottish wildcat. But these aren't hybrids in strict terms because they are all the same species, just different subspecies. In other words, domestic cats and wilcats are both the same species, pure and simple. There are some variety of domestic cats such as Bengal cats that were produced using deliberate hybridisations with other cat species, in the case of the Bengal, with Asian wildcats Prionailurus bengalensis, but these are "boutique" varieties and have contributed nothing at all to the vast majority of domestic cats. Furthermore, these domestic/wildcat hybrids can only be kept as pets if the wildcat parent is at least three generations back from the pet cat being sold; otherwise it is just too aggressive and unfriendly. So even a Bengal cat -- nominally a hybrid in the popular if not scientific sense -- will have only have one-sixteenth the genes of Prionailurus bengalensis and all the rest will be Felis sylvestris!
Cattle
Darwin's approach to the origins of cattle has long been rejected on the basis of DNA evidence. Cattle were domesticated from Bos primigenius, the animal known as the aurochs, though likely from different subspecies in different parts of the world. As with species of Canis, species of Bos sometimes hybridise, but just as with dogs, these hybrid Bos variants have not contributed to the gene pool of the cattle kept on farms. Your average milk or beef cow is pure "aurochs" in its genes.
Plants
Hybridisation is really only significant with domesticated plants rather than animals. Wheat was produced by a famously complicated set of hybridisations. Roses (such as "hybrid teas") are famous hybrids as well. Unlike animals, which rarely hybridise in the wild, plants hybridise naturally all the time, and the resulting "hybrid vigour" is a well known effect much utilised by farmers and horticulturists.
Personal thoughts
Within the fishkeeping hobby, there are several species that are likely hybrids in reality, though the amount of hybridisation may be variable. Swordtails, platies, mollies, discus and angelfish are good examples of species considered "a" species but likely produced back in the 50s and 60s with careful crosses that helped stabilise the bright colours fishkeepers wanted. But most other standard community fish likely are true species in all practical senses: tetra, barbs, Corydoras, plecs and so on. African cichlids are a special case because they are so successful at rearing their fry in community tanks. As a result irresponsible fishkeepers have flooded the market with garbage "mixed African cichlids" making it very difficult to get pure species of certain species (Pseudotropheus and Aulonocara especially).
Personally, I have no objection at all to people hybridising fish if they want to, though I do object to hybrids like red parrots that are distorted away from the normal body shape. But that dislike holds for fancy goldfish (a true species) as much as, say, balloon mollies (another hybrid). My disgust is directed much more at people who hybridise fish and then off-load unwanted fry on retailers and other hobbyists. These people have created a massive problem for those of us who care about the hobby generally and not just ourselves. Misidentified "mixed African cichlids" are impossible to give advice about in terms of social behaviour and maximum size, and also make it very difficult for people to create balanced, attractive aquaria containing varieties of known appearance and temperament.
Cheers, Neale
Canis familiaris had been crossed with wolves, coyotes, and several other wild dogs hundreds if not thousands of times to produce and modify existing breeds, many of those crossings are well documented, and the ancient domestic stock originated in multiple parts of the world. The origins of domestic cats is largely unknown, but many modern breeds were produced by crossings with wild species. Darwin cataloged the origins of domestic cattle hybridized from multiple wild species in the 18th and 19th centuries.
It's a hybrid similar to the normal parrot but usually larger with a more round appearance and flat head area, usually they also have more 'normal' mouths.
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