Note added February 8, 2021: An example of a rare, high-consequence event occurred today in India: a chunk of a Himalayan glacier broke off and unleashed a flood that took out one dam and seriously affected another, took out two hydroelectric power plants and killed at least 14 with another 170+ missing. This is not only an example of a rare event, but also of a compound event: a piece of glacier fell off, created a wall of water and mud that barrelled down a valley, and destroyed dams and infrastructure. It is also a combined natural disaster and engineering disaster. More info here.
As a member of the Resilient America Roundtable of the National Academy of Sciences, Engineering and Medicine, I gave a presentation in February 2019 about low-probability events with high-consequences should they occur. Here I summarize that presentation, giving examples of such events and suggestions for research, educational, and organizational challenges. Examples that we most commonly think of when considering "rare" events are big hydrologic floods, floods from dam failures, volcanic eruptions and ash clouds, earthquakes and earthquake-induced tsunamis, landslides, and wildfires. Less frequently considered are solar eruptions with the ejection of coronal material (CMEs), meteorite impacts and combination events (e.g., and earthquake plus a tsunami in the midst of a pandemic.
Natural floods (Mississippi River): For reference, during the recent "catastrophic" flood of the Mississipi River in 2008 that severely damaged Cedar Rapids (Iowa), the discharge at St. Louis was about 700,000 cfs. In the Great Flood of 1993 it was 1,030,000 cfs and in 1844 it was 1,300,000 cfs.
Natural floods (Colorado River, Grand Canyon), see attached graphic: The catastrophic flood on the Colorado River in 1983 that nearly took out Glen Canyon Dam and caused serious environmental and geomorphic changes for nearly 300 miles, had a discharge of ~100,000 cfs. For comparison, the discharge of the 1884 flood was about 300,000 cfs and a flood in about 550AD had a discharge of ~500,000 cfs.
Unnatural floods: With the aging infrastructure of U.S. dams, we should remember the 1889 Johnston Flood (Pennsylvania) that killed 2209 people in 10 minutes; the St. Francis Dam failure in Los Angeles that killed 600 people in 1928; the 1996 Teton earthen dam failure in Idaho that caused $2B in damages, and the 2017 Oroville Dam problem in which a drenching rain filled the reservoir to 151% of normal capacity causing erosion of the interior of the dam and the emergency spillway.
Volcanic eruptions: Volcanologists have created the logarithmic Volcanic Explosivity Index (VEI scale) to express the potential magnitude/disruption of volcanic eruptions akin to the Richter (and other) scales for earthquakes. For reference, the 1980 eruption of Mount St. Helens was a VEI 5, considered "large". VEI 6 and 7 events are considered "very large" and volcanoes believed to be VEI 6-7 are Crater Lake (Oregon) and in Alaska: Novarupta in the Valley of 10,000 Smokes that erupted in 1912; Churchill, Okmok, Neniaminof. VEI 7 eruptions in the past were Santorini, Greece' Tambora, Indonesia; Valles Caldera, N.M., and the Phlegraean Fields, Naples, Italy. Eruptions in Alaska, Kamchatka, and Iceland can routinely erupt and produce economic chaos, e.g., the disruptive eruption of Eyjafjallajokull in Iceland was a VEI2.