The best example I can think of did not involve a catastrophe before, but between 1853 and 1870, Georges-Eugène Haussmann, under the direction of Emperor Napoleon III, oversaw a series of vast public-works projects that "renovated" the city of Paris.

These "renovations" saw the demolition of much of the surviving mediveal-era buildings, as well as the remnants of the city walls. In fact, much of the street grid of inner arrondistments was totally rearanged, as buildings were demolished to create wider, straighter, streets with "fewer" broken alleyways. In their place was created the modern center of Paris, as it currently exists, with broad avenues and a unified 2nd-empire architectural style that still predominates the center of Paris. The plans that Hausmann drew up continued to be used as the basis for urban planning in Paris well into the 1920s. The wiki article gives a good overview, but is entirely unsatisfactory.

Compare the following three maps of the city of Paris, from 1800, 1864, and 1892, in the following imgur album to see what I mean: http://imgur.com/a/2aLW2

One in particular, which is the source of much historical speculation, is the notion that Nero was responsible for the burning of Rome in 64 AD. Champlin's book on Nero features a chapter, number 7 "Great House", that goes into this in great detail. As a controversial figure, Nero was blamed for setting the fire, but there were many other possibilities. Beyond his possible culpability, Nero did redesign Rome after the fire. Some of the changes were intelligent improvements that would prevent another fire from destroying such large areas of the city in the future, spacing homes further apart, using fire-proof concrete as the primary building medium, careful placement of fire fighting tools and water sources, as well as restoration and rebuilding of temples and other structures that were destroyed or damaged.

But, his construction of the Domus Aurea in a huge section of the city as his personal pleasure palace was controversial. This structure took up a massive lot of real estate that had been home to many wealthy homes and was ostentatious in the extreme. It wasn't just a massive palace, but also featured a lake and park grounds, as well as a colossus of Nero himself. Though the grounds were largely a public space, the Flavians "returned" the land of the Domus Aurea to the Roman people by constructing the Colosseum where the man-made lake once stood.

You can find more information on Nero's rebuilding of Rome in "A History of Roman Art" by Fred S. Kleiner and in the "An Oxford Archaeological Guide to Rome" by Amanda Claridge

Yes, it did happen. E.g. I'm currently living in Dresden, which was bombed right at the end of the war. (It's not clear whether it was done purely out of a desire for vengeance or whether the western allies didn't want it to fall into soviet hands intact.) When they rebuild, the east german government went with a very soviet style of of urban planning. There is a very stark contrast between the wide open avenues (lined with highrises) that cross the inner city and the areas that had survived the bombs. One of the beneficial effects of this is that rush hours isn't nearly as bad as in other cities. You are right in suspecting that the economy wasn't strong enough to support that rebuilding effort, which is why it took quite a while to finish. In fact, the city is still in the process of reconstructing the historic center.

Another cities that was rebuild is Athens. (The original one in Greece.) After the Greek had won their independence in 1821, the powers of Europe put a bavarian in charge as their king. The guy really wasn't impressed by the small town the great Athens had turned into, so he had a new capital build on its place. It was very modern for the time and featured wide avenues to ensure good flow of traffic. Unfortunately, Athens was not expected to ever grow beyond 100000 people and the car had not been invented, yet. Nowadays the city is massive and the greater metropolitan area of Attika might be home to as many as 5 million people, though nobody is quite sure.

The main issue is that fire or earthquake don't change property lines, so streets can't be widened or rearranged very easily. Thus Wren's schemes came to nothing; and nothing changed in Chicago after the 1871 fire, nor in San Francisco after the 1906 disaster, nor Homestead, Fla., after Hurricane Andrew. Dresden under Soviet control, or Paris under Napoleon are very different legal environments than the Anglo-American tradition.