Video Credits: YouTube EmbarkToHeaven

Promotional poster of the movie 2012.
1806: Prophet Hen of Leeds - Someone said that in the town of Leeds (now a city of United Kingdom), there is a hen laying an egg 0n which the words "Christ is Coming" is printed or written. A curious local watched the hen and the eggs and found out that the phenomenon is just a big hoax.
1910: Halley's Comet - An astronomer discovered that the tail of the Haley's comet contains a deadly toxic gas cyanogen or simply cyanide. The panic started when it was discovered that the tail of the comet will pass through earth. Nothing happens as the comet passes by through the skies of the earth.
1997: Heaven's Gate - When comet Hale-Bopp appeared in the skies of the Earth (probably the only comet I've seen so far), a cult named Heaven's Gate speculated that a UFO is following in its tail and NASA is responsible for the cover-up. Astronomers or even people with telescopes can prove that this speculation is not true. Their little world ends as they committed suicide (all of them) on March 26, 1997.
These three failed doomsday predictions are just a condensed form of the article "10 Failed Doomsday Predictions" from Live Science.