Rocks from the sky: Ernst Florens Friedrich Chladni is usually called the father of meteoritics. In 1794 he published a book that declared that not only are meteors stones that fall from the sky, but they originally come from space. After a spectacular fireball and meteorite recovery in Weston, Connecticut, in December 1807, Thomas Jefferson, then the president of the United States, responded with great skepticism: "Gentlemen, I would rather believe that two Yankee professors would lie than believe that stones fall from heaven." By the late 1800s meteorites were established science thanks to studies of a number of meteor falls. The first time an impact theory was proposed was in 1891, but even by the 1950s there were still many scientists who doubted this proposal, even to explain the craters on the Moon. In 1963 geologist Eugene Shoemaker became the first scientist to prove conclusively that the famous Barringer Crater in Arizona is actually a meteor impact crater caused by the explosion following an impact, and not a caldera or volcanic steam vent.
Status: Phenomenon is established science, and its explanation is also established science.
Ball lightning: Bouncing balls of light after a lightning storm have been reported for centuries, but only since about the 1960s have scientists started to carefully study them and discover that not only are they real and not fictions of folklore, but they are very hard to understand. There have been international scientific symposia devoted to this subject, and numerous technical articles published over the last 40 years. What once was the subject of folklore has now become established science, though a detailed explanation for how these balls of plasma are produced and remain stable for many minutes still remains elusive.
Status: Phenomenon is established science, but an explanation for it is still being developed.
Ball lightning as depicted by C. Flammarion in 1873
Earthquake lights: An earthquake light is an unusual luminous aerial phenomenon that reportedly appears in the sky at or near areas of tectonic stress, seismic activity, or volcanic eruptions. Once commonly challenged, it was not until photographs were taken during the Matsushiro earthquake swarm in Nagano, Japan (which occurred from 1965 through 1967), that the seismology community acknowledged their occurrence. During the 2007 Peru earthquake lights were seen in the skies above the sea and filmed by many people. Video footage also recorded this happening during the 2011 eruption of Sakurajima Volcano, Japan. The most recent model suggests that the generation of earthquake lights involves the ionization of oxygen in some types of rocks by the high stress before and during an earthquake. The ions travel up through the cracks in the rocks. Once they reach the atmosphere these ions can ionize pockets of air, forming plasma that emits light. Lab experiments have validated that some rocks do ionize the oxygen in them when subjected to high stress levels. A different explanation involves intense electric fields created piezoelectrically by tectonic movements of rocks containing quartz.
Status: Phenomenon is established science, but the explanation for it is still being developed.
Spontaneous human combustion: Spontaneous human combustion (SHC) is the alleged process of a human body catching fire as a result of heat generated by internal chemical or nuclear action. A more reasonable theory of how human bodies burn in rooms without having the entire room engulfed in flames is the idea of the wick effect. The ignition point of human fat is low, and getting the fire going would require an external source. Once ignited, however, a "wick effect" from the body's fat would burn hot enough in certain places to destroy even bones. To prove that a human being might burn like a candle, Dr. John de Haan of the California Criminalistic Institute (California Department of Justice) wrapped a dead pig in a blanket, poured a small amount of gasoline on the blanket, and ignited it. Even the bones were destroyed after five hours of continuous low-temperature smoldering. The damage to the pig, according to Dr. De Haan, "is exactly the same as that from supposed spontaneous human combustion."
Status: Phenomenon is considered controversial and not widely investigated due to there only having been a handful of cases over the last 100 years, and due to the enormous stigma associated with it thanks to the bizarre "tabloid format" way in which the rare cases are reported. A science-based explanation that can account for many of the observable features (e.g., the wick effect) may exist, but there may be multiple phenomena all loosely termed "spontaneous human combustion," so one explanation may not apply to all situations.
Crypto-organisms: Is the Loch Ness Monster really a plesiosaur? Is there a dinosaur running around in the Republic of Congo? The list of "hidden" animals totals over 200 specimens drawn from mythology and eyewitness accounts. These include the Kraken from Greek mythology, Yeti, Sasquatch, and my personal favorite, the Jersey Devil. Many amateur investigators keep this subject alive by doing field studies with elaborate video equipment and capture poorly focused or controversial images of what seem to be the legendary creatures. They have been spurred on by such things as the famous discoveries of "living fossils," such as the coelacanth, discovered in the western Indian Ocean in 1974. The list of confirmed living fossils discovered and verified by scientists contains over 80 species, including the oldest of them all, the 3.5-billion-year-old stromatolite (found in Shark Bay, Western Australia, among other places). Many species of insect in your backyard have been around for over 100 million years.
Status: Phenomena include many legitimate organisms, but the phenomenon is delegitimized by including creatures from folklore with equal weighting; explanations for the existence of known "living fossils" are based either on, for example, slow evolution (e.g., insects, stromatolites), or on being isolated from easy predation, especially by humans (e.g., sharks, coelacanth).
So there you have it. Even controversial ideas have their place in the conversation about how the world works. They give us something to wonder about, and wondering about things is good!