If Disasters are enabled in the difficulty settings, random disasters will occasionally happen. Disasters are not the same as vehicle crashes - for more information about these, see the individual vehicle pages.
1930-1955: A zeppelin appears on the border of the map and flies through. If the zeppelin happens to go over an airport, it will crash. The wreck of the zeppelin remains on the runway, blocking this airport for half a year.
1940-1970: A small UFO will fly around, looking for one of your road vehicles. When it finds one, it will fly down, the road vehicle will break down, and be destroyed.
Oil refinery explosion
1960-1990: A military aircraft will fly on a predetermined straight path and destroy an oil refinery. The industry will be rebuilt though, so no real harm is done. Goods production will be delayed while the industry is rebuilding.
1970-2000: A Military Helicopter will appear on the map and travel in a straight line towards the factory on its line of movement, and will fire rockets at it, causing the factory to be destroyed. However, like the above "Oil refinery explosion", the factory will be rebuilt after a short period of time, during which goods production will be delayed.
2000-2100: A large UFO will fly around, looking for a section of non-AI railway tracks to land on. In case there is no railway to land on it will land on a randomly chosen tile. When large UFO lands, it causes nearby trains and road vehicles to break down regardless of the breakdown setting. A military aircraft later comes and drops a bomb on it, destroying it along with nearby buildings, trees, and unoccupied railway tracks.
If you look closely on the military aircraft, you can see the X-Com sign. That's because it is actually the Skyranger craft from Microprose's (TTD's original producer) 1993 Enemy Unknown X-Com game. The Large UFO is also reminiscent of the Harvester UFOs from it.
Coal mine subsidence
1950-1985: A shaft at a coal mine will collapse. Anything on a line, extending a random number of squares, will be destroyed - railway tracks, trees, farmland, town buildings, etc.
Don't believe the rumours they destroy ships or oil rigs - they aren't really a disaster (although that may have been the original concept). They are more spoofs from Terror from the Deep X-COM: Terror from the Deep, which was coming out at the time.
1940-1965: Small submarines. Quite rare.
1975-2010: Larger submarines. Notably larger and a little less rare.