an example of hybridisation with-in a plant species is the wheat and rye hybrid tritacle. the purpose of the hybridisation of wheat and rye was to produce an offspring with wheat's high yield, and favourable baking qualities, and rye's tolerance of harsh climates and ability to thrive in soil of low quality.
there also exist tigons: hybrids of male tigers and female lions, and ligers: hybrids of male lions and female tigers, which i find amusing - although i don't know of the reason for the hybridisation.
in addition, there are dog hybrids, such as the the labra-/golden- doodles; hybridised for a labradore's traditional role as a service dog and a poodle's low shedding and hypoallogenic qualities. also, the wolf-dog, although they aren't technically hybrids as they all belong to the same species (Canus lupus and C. lupus familiaris).