I expect we'll have to keep this to the Western world, but what was the first dance to take the world by storm? These days we have a huge variety of them -- thanks to the internet -- that crop up all the time, from twerking to daggering. But this phenomenon must be quite old, indeed.
What was the first dance to take the world by storm, and how did it gain popularity? How was it viewed by the establishment?
I can't really tell you exactly what it looked like, but Greek dancing certainly took off under the Late Roman Republic and the older generations completely disapproved of it - hated it in fact, which for me makes this very relevant. Generational disapproval is a big part of dance crazes, I think.
Here's a source to get you started, from Macrobius:
They learn shameful arts, along with cinaeduli [the diminutive of cinaedus, which means 'man who likes to take it up the arse' basically], and carrying their sambuca and psalter [Greek musical instruments], they attend the entertainers’ schools and they learn singing – all these being things that our ancestors wished to be judged disgraceful for freeborn persons. They attend, I repeat, the very dancing schools – unwed girls and freeborn lads among the cinaedi! Though someone might have reported these doings to me, I could not have taken in the notion of noblemen instructing their offspring in these things. Yet when I was conducted to a dancing school, by Jove, there I saw more than fifty boys and girls in the school, one of them a boy (and this caused me the sharpest pain, on our state’s behalf), a boy marked out as noble, the son of a candidate for public office, under twelve years of age, dancing to castanets such a dance as some shameless little slave could not decently have performed. Macrob. Sat. 3.14.7
Roman moralisers tended to elide dancing, singing, actinga and other performance-related activities with prostitution - as you were putting yourself out there for money.
The same activities disapproved of in moralising texts seem to be celebrated in a lot of Latin poetry written by younger poets. Propertius here mentions dancing - it's almost definitely the Greek style as Greek culture is a big focus of his and other similar writers. He links it with the rest of the 'luxurious life' which Roman authors saw as distinctively Greek. Sorry for the olde-time translation:
Let night speed mid the wine-cup, and let the casket of yellow onyx make glad our nostrils with oil of saffron; let the hoarse pipe blow for the midnight dance till it give o’er for weariness, and let thy wanton words come fast and free. Let the merry banquet keep unwelcome slumbers far, and let the air of the neighbouring street ring loud that all may hear. Let us cast lots, let the fall of the dice reveal to us those whom the boy god lashes with heavy pinions. And then when the hours have been sped by many a goblet and Venus appoints these mysteries that wait on night, let us with all solemnity perform the anniversary’s rite in our chamber… Propertius 3.10.22ff