A Legendary pokemon called Mew. It is said to share the DNA of all Pokemon.
It can be caught if you bring an Old Sea Map to Lilycove City. This lets you go to Faraway Island, where it can be found.The Old Sea Map can be obtained though certain special events such as Anniversary 1 and 2.
It has several variations, such as Mew Ying, Yang Mew, and the Trollface Mew. Each is different in various ways.