In biology, hybrid has two meanings. The first meaning is either the offspring of two different species, or of two different genera. The second meaning of "hybrid" is crosses between populations or cultivars ("cultivated varieties") of a single species. This second meaning is often used in plant breeding. Hybrids between species of the same genus are sometimes known as interspecific hybrids or crosses. Hybrids between different genera are sometimes known as intergeneric hybrids.
Ernst Mayr wrote of Gregor Mendel, "He was uncertain about the nature of the kinds of peas he crossed, and, like most plant breeders, he called heterozygotes "hybrids." When he tried to confirm the laws he had found by using "other hybrids" that were actually real species hybrids, he failed. The use of the same term "hybrid" for two entirely different biological phenomena thwarted his later efforts." (This is Biology, 1997, p58f).
Plant hybrids, especially, may or may not be stronger than either parent variety, a phenomenon which when present is known as hybrid vigour. In animals, hybrids often manifest reduced fertility or, like the mule are sterile.
Beefalo, a cross of an American Bison and a domestic cow, this is a fertile breed, despite the two species being classified in different genera (Bison and Bos, respectively).
Wolfdog, the cross between a domestic dog and a Wolf. Crosses also occur between coyote, wolves, dingos, and domestic dogs. Many of these produce fertile animals ("dog" & "wolf" are now usually considered the same species, so this may be considered a non-hybrid).
Hybrids btween spotted owls and barred owls
Liger (or Tigon, depending on the parents' genders), a cross between a Lion and a Tiger. Various other wild cat crosses are known involving Lynx, Bobcat, Leopard, Serval, etc.
Cama, a cross between a Camel and a Llama, also an intergeneric hybrid.