There are many refrences to mythology in anime. One myth that frequently appears in anime in various forms is the "Four Saint Beasts" also known as the "Four Gods". These four were originally from China but made their way to Japan, where their names were changed to Suzaku, Genbu, Byakko, and Seiryyu.
This is only the tip of the ice berg for the representation that are the Saint Beasts. In anime they are often seen in animal form: a red bird (similar to a phoenix), a black tortoise (sometimes shown with a snake), a white tiger, and a blue dragon. Direction also comes into play, Suzaku for the South, Genbu for the North, Byakko for the West, and Seiryyu for the East. The directions then in turn represent the season, Summer, Winter, Autumn, and Spring.
These beings show up, in some form or another, in many anime series. The strongest and most obvious is Fushigi Yugi (Mysterious Play). Here we have Miaka, a typical, clutzy, always hungry, high school girl. To make things short she gets sucked into a book where she becomes the priestess of Suzaku and has to find a way out. We have the four gods, in their respective direction, and they're followers (the seven that the priestess has to gather) have constellation names.
My first encounter with these characters, though, was in the series Yu Yu Hakusho, the Beasts of Maze Castle arc. To destroy the flute that was controlling demon insects on earth, Yusuke and company have to enter Maze Castle and confront its guardians. Though they are not named in the series it is obvious by their design who they represent. Genbu is made of rock with a turtle-like shell, Byakko is a bi-pedal white tiger, Seiryyu was a guy with a blue dragon design on his clothes. Suzaku has a red outfit and an annoying parrot lackey.
In the Descendants of Darkness (Yami no Matsuie), Tsutzuki is able to summon the Beasts to do his bidding. In the anime they pretty much attack his enemies, in the manga they are given more "air time", so to speak, where they have their own personalities and they give Tsutzuki advice.
This is just a sampling of some series that show these characters. Whenever you see these animals this is the reference they are making.
Boma at 9:53 PM