Animal marriage
History
The practice of animal-human marriage has made appearances in several mythological stories and folklore, and is often understood to mean a deity-human marriage involving gods or heroes. The Chinese folktale "The Goddess of the Silkworm" is an example of a tale where a woman marries a horse. A similar Irish legend tells of a king who marries a horse, symbolizing a divine union between the king and the goddess of the land. Also, the indigenous Cheyenne has a story of an animal-human marriage in "The Girl who Married a Dog". In addition, there are many Native American stories about people who married animals. In these Native American myths, animal spirits frequently assume human form. They are not seen as literal animals, but representatives from the animal kingdom.
In Reality
In Hinduism, some cultures will marry their dog as a protection ritual for their future human husband.
In Practice
Some zoophiles will get married to their pet through a variety of means. The site MarryYourPet is one of these examples. There is also the Circle of Joining ceremony that includes multiple zoos in the marriage process.
Legality
Unfortunately, there are no laws that make this technically legal however it is nice that you are married in the eyes of the community to your loved one.