Sociologically speaking, our species is just recently getting hip to the fact that sex is not an either/or binary proposition. That's sex as in gender, and the animal world has been cool with this all along. Hundreds of species are born intersex, meaning they possess both male and female sexual characteristics. Some humans are born this way, too.
And there's plenty of variation in between. Way down on the food chain, animals like earthworms and snails exhibit "simultaneous hermaphrodism" - they have both ovaries and testes, which simplifies mating rather nicely. Other critters have "sequential hermaphrodism" and can essentially self-induce a biological sex change in particular circumstances. Indeed, sex is a magnificent spectrum in the animal world - Jules Suzdaltsev has the details in today's DNews report.
Phys.org: Self-fertilizing worms lose thousands of active genes in reproduction process
PopSci: Androgynous Lionesses Strut and Roar in Manly Manes
Scientific American: Strange but True: Komodo Dragons Show that "Virgin Births" Are Possible