These would generally be more of a problem for fortresses rather than adventure, but it could still be entirely possible to stumble upon one in adventure mode.
They would be pretty rare in general, so don't count on one always happening in a game
Natural disasters would of course affect sieges as well, so depending on how well prepared you are a natural disaster could actually be a gift from the RNG
Hurricanes and Flash Floods
-Only appear in coastal or low-lying areas
-Mass flooding, storms
-Dwarves and animals can be swept away entirely, or drowned, by the rush of water
-Proper drainage would be essential, to prevent water from completely flooding the lower areas of your fortress.
Avalanches
-Only appears in more mountainous areas
-Rocks start sliding down from higher elevated areas, crushing all in their path
-Keep everyone inside
Volcanic Eruption
-Obviously only happens in areas close to a volcano
-Magma everywhere, torches everything it touches
-Extremely rare
-After the initial magma release, clouds of ash and soot cover the land and temporarily block out the sun, destroying outdoor crops
-These are extremely rare and also extremely devastating, but there needs to be some more risk with setting up a fortress by a volcano
Tsunamis/
-Also known as tidal waves
-Unlike hurricanes and flash floods, which are more like sustained flooding and giant storms, a tidal wave would be one enormous wave of water smashing into the coast
-Coastal areas only
-Still a potential for flooding
-Keep everyone inside, ensure proper drainage as well
Earthquakes
-Large breaks in the land, shifts, etc.
-Really a chance of happening anywhere
-Dwarves, animals, items, and even buildings could get thrown around by the shaking
Tornadoes
-Also called twisters and cyclones
-Rare chance of occuring anywhere
-Very high-speed windstorm capable of sucking just about anything up into the air.
-Keep all your dwarves inside and underground
Lightning Storms
-Not exactly a "natural disaster" but something that could be good to add
-Intense rainfall, high winds
-Small chance of lightning striking a random spot, could potentially take out a dwarf or an animal