The logic for this lies in the historical trend that the same geographic locations that help a civ grow faster (rivers, mineral rich mountains, fertile plains) also put "speed bumps" in the path of their growth (all the catastrophes mentioned above.) A natural catastrophe would destroy certain city improvements and reduce the city's population, requiring them to be rebuilt and repopulate over time. Below are a few examples of Wonders being destroyed by natural catastrophes:
Lighthouse of Alexandria: destroyed by earthquake
Great Library of Alexandria: while many scholars continue to repeat that it was burned by the Romans, it is much more likely to have burned from the fires that inevitably follow an earthquake. Alexandria has been shown by recent archaeological discoveries to have been rebuilt many times following earthquakes.
Temple of Jupiter (at Athens?): destroyed by earthquake
Temple of Artemis: arson (okay, so its not natural, but a nut with a torch is still a catastrophe)
Hanging Gardens: flood? I'm not sure on this one, but since it was made of mud bricks and built on a flood plain, this makes sense.
Tomb of King Mausoles(sorry if I misspelled his name): earthquake
Colossus of Rhodes: earthquake after standing for less than 60 years

What do you think?

One thing is that it could be used by Firaxis to keep people from getting to powerful. Got a large city long before anyone else? Have the game burn it.

I think the earthqaukes should have radius's, and there should be three levels, first level would be say...2-3 square radius, and it only destroys one improvement in the closest city. lvl 2 would be 4-5 square radius, and would destroy one improvement in the two closest cities. and would have a 50% chance of destroying a second improvement. the third lvl would be the worst, it would have a 6-8 square radius, and would automatically destroy one improvement in the three closest cities, plus a 50% chance of destroying a second improvement. and a 50% chance of killing one citizen in each of those cities.

also, all units within a earthquakes radius when it happens, depending on the lvl, is killed. for the first lvl, it would have a 50% chance of being killed. second lvl, 75% chance. and the third
would automatically kill any and all units within radius.

this may souond a bit too vierce, but it is realistic. earthquakes would be random, as would their sizes.

for floods, if your city was next to the sea or river, then it would be flooded during floods. when a city is flooded, its production is slowed by half for up to five turns. floods would also be random, but only on rivers and ocean shores

there should be a new tile improvement also, a volcano, it would erupt say...every 500 years. or at random. a city next to it would have a 50% chance of losing a citizen, and an improvement.

Gammaray fan,
What exactly do you mean by natural wonders? Are you advocating the SMAC landscapes that gave the holder extra resources, trade, food, growth, etc.? Or something different?

As for disasters, yech. As long as the potential for disaster is toned down, I don't mind too much, and as long as there are ways to protect your precious cities in the late game. But for the most part, disasters are just another way to screw people with bad luck, like me . If you must implement random events, you have to balance them out with minor positive events.

an Alien Ufo crash would be fun.. (like with Roswell)
and how about Snow Blizzards or an extremely cold winter in arctic regions
that kills some population (its silly you can settle on the arctic so early anyhow) ..

I deffinatly think that disasters should be readded, and made more powerful. But together with making them more powerful there should be buildings that can be built to ward off disasters, and tech to do likewise. Earthquake resistent buildings like in Los Angeles, or levies to protect against floods and whatnot.