In Asia, the snake was close to the divine dragon. In Indian mythology we have the Nagas, great dragon-like serpents, who possessed many magical powers and guarded great treasures. In Buddhism, Nagas were believed to be both water-dwellers, living in streams, and earth-dwellers, living in underground caverns. They also guarded Mt. Sumeru, the Axis Mundi. In the legend of the Buddha's life we encounter a naga called Mucalinda - when Sakyamuni sat meditating under the Bodhi tree, a heavy rain started and Mucalinda with his seven snake heads formed a sort of umbrella above the Buddha's head to protect him from the elements.
[Pilgrimage to the Cave Shrine of Benzaiten by Hiroshige (c. 1850)]
Perhaps because of the "Naga treasures," the snake is also associated with money and profit - on New year cards we often find it accompanied by gold coins.
Japan knows many snakes (as anybody who has hiked in Japan's forests can attest to); they are an ingredient in traditional medicine. Dangerous is the mamushi, the pitviper, whose bite leads to several deaths each year (another venomous snake is the habu, found on Okinawa).
The Year of the Snake is associated with the earthly branch symbol 巳 (mi), and this is how it is written on New Year's cards.