The crane (a bird) is a traditional and beautiful origami. The pattern is often included in origami paper packs. There are a few variations, such as the flapping bird; however I like the design linked below because it gives the crane some body and delicate, thin tail and neck.
The crane is considered to be a mystical and holy creature which is said to live for a thousand years. Different stories state that folding 1000 cranes will grant a wish, eternal good luck, long life or recovery from an illness.