I've only been through rather minor ones, such as small earthquakes (enough to shake the house a bit, and knock stuff off shelves); hurricanes (not the epicenter, but still a ton of `high winds and flooding--think Hurricane Agnes); tornadoes (didn't come to our house, but was sighted in the area--this happens about once a year), minor flooding; major snowstorms (no heat/power for 5 days). When Three Mile Island happened, I was a kid, and we were to be the next load of evacuees, but they got things under control before that happened. We were sweating it out--my cat had just had 4 kittens the week before, and Mom & Dad were worried where we could go, and still keep them with us.
I still live near 4 nuclear power plants, within 100 mile radius, and it makes me a tad concerned sometimes.
I always keep disaster prep supplies handy and updated. No, I don't spend my days chewing my fingernails with worry. I just acknowledge that bad things can happen, I want us to be ready for them. DH & I include our cats in that statement, BTW. We're not leaving them behind, should we ever need to evacuate. If they can't go, we don't go. Fortunately, after Hurricane Katrina, there was a push to have a lot more pet-friendly shelters.