All kinds of weird and terrible things can happen to a building during a natural disaster, but just because a building looks like it has gone through an earthquake, tornado, or even some type of bizarre wormhole doesn't mean the structure is unsound or that anything ever even happened to the building. In some cases, architects were merely taking a risk and designing structures that are only meant to look damaged. One example is Chile's Errante Guest House, seen above.
Perhaps some of the most famous examples of this concept are a few of the Ripley's Believe It or Not Museums around the country. It's hard to think of any building exterior that says "believe it or not" more than a functioning museum that looks like it has completely flipped over (complete with a car crushed under its weight).
You can see more buildings like this over at io9.
Primary image courtesy Flickr user Sue-W.