The legend of Atlantis is actually based on the notes of a Greek named Solon, who travelled to Egypt several generations before Plato's time. While in Egypt, Solon visited a priest at the temple of the goddess Neith. According to Solon's notes, he was told that the Greek civilization was too young to know much about history (only a few hundred years at the time), while Egypt had seen many other cultures come and go. The priest claimed that each time a culture passed away, some new culture would rise up and think itself to be the first. He then showed Solon astronomical records of every solar and lunar eclipse which took place over the previous 10,000 years (if this is true, this would dramatically affect our own view of the history of civilization). Finally, the priest made a specific example of a culture which had been very advanced, but had vanished beneath the waves in a tremendous cataclysm less than 1000 years before.
Fast forward several generation to Plato, who reads Solon's account of his travels, and pens the Atlantis story, not as history, but as a moral lesson against impiety. In HIS version, he claimed that Atlantis was destroyed, not as a result of a natural disaster, but because the gods were offended at their behavior, in much the same way that Sodom and Gomorrah were said to be destroyed because they offended a different god.
The problem is that readers in later generations didn't understand that Plato was writing a moral lesson, not a historical account. They just swallowed it whole, exactly as written, without allowing that Plato might not have all the facts straight, or if he did, that he might not introduce his own spin on the story.
Among geologists and archeologists, the most favored probable basis for the story is the destruction of the Minoan culture, whose capital city was destroyed by the eruption of Thera (also called Santini), around 1350 B.C.E. The Minoans were quite advanced culturally and technologically, as far as we can tell, they didn't have nuclear power or antigravity, but they were considerably ahead of even the Egyptians, with hot and cold running water and indoor toilets, which wouldn't be duplicated even during Platos lifetime, nor for several hundred years more.
The hypothesis of the crust rapidly slipping around the mantle is not widely accepted among geologists, because the shear strength of the rocks binding the crust to the mantle is viewed as being too high to allow it to move separately. The slow movement of the crust as a result of plate tectonics is widely accepted, however, although it wouldn't contribute to the Atlantis story.
A very interesting account of archeological findings on Thera and how they relate to the Atlantis story can be found in "Unearthing Atlantis" by Charles Pelligrino.