Budai (布袋) is a deity from Chinese folklore. Most notable in the West for being constantly confused with the Supreme Buddha, Siddhārtha Gautama. Most notable in the slightly more culturally aware West for introducing the idea that in many traditions, there is more than one Buddha.
Budai is most commonly depicted as a short, fat, laughing man, wearing a robe and carrying prayer beads, and sometimes also a cloth sack in which tradition says he carried all of his worldly possessions. According to tradition, Budai was an eccentric Chinese monk in the early 900s who wandered the land, being generally jovial and kind to people, especially children and the elderly.
At the same time, he was a font of wisdom; he is also known as The Awakened, a reference to having achieved Enlightenment. A famous Zen koan regarding Budai goes like this:
Budai traveled the land giving candy to children, asking only for a penny now and again from Zen monks and lay people. One such Zen monk stopped him on the road, asking, "What is the meaning of Zen?" Upon which Budai dropped his bag and stood silent. The monk decided to rephrase his question, asking, "How does one realize Zen?" Upon which Budai picked up his bag and continued on his way.
Many place Budai as a Buddha or bodhisattva himself, with some believing he was an incarnation of the future Buddha. This latter belief is supported by his supposed last words, a short poem:
Maitreya, the true Maitreya
has billions of incarnations.
Often he is shown to people at the time;
other times they do not recognize him.
Aside from his place in several Buddhist hierarchies, he is one of the seven lucky gods of Taoism. It is from here that the notion that "rubbing the Buddha's belly brings good luck" is derived.
He has also gradually (over the centuries) replaced or been melded with many, many local deities and heroes, and is often confused for several others. For example, he may be one and the same as the Japanese Hotei - almost as if he were wandering the land, passing through but never staying.