In a certain sense, 1953's The Beast from 20,000 Fathoms was the movie that started it all (although some purists believe that only Japanese films should count as kaiju). Sure, there was King Kong in 1933 and various other creature features along the way, however, this American production came out the year before the original Godzilla and helped inspire the more famous Japanese film that followed.
The Beast from 20,000 Fathoms opens with atomic testing in the arctic circle. The blast awakens a hibernating dinosaur, the entirely fictional Rhedosaurus. The huge creature makes its way down the North American coast, wreaking havoc as it returns to its ancient spawning ground, which just happens to be in New York. There's not much to the story. It's a pretty standard 1950s tale of a bunch of stiff white guys trying to stop a monster. What makes The Beast from 20,000 Fathoms stand out, even today, is the special effects.
The Rhedosaurus was created and animated by Ray Harryhausen, protégé of Willis O'Brien, the legendary stop-motion animator who brought the original King Kong to life. In the decades to come, Harryhausen would become a special effects legend in his own right, creating stop motion creatures for films like Jason and the Argonauts and Clash of the Titans. As for the Rhedosaurus, he never returned for a sequel, but the whole idea of a huge creature awakened or created by an atomic blast definitely caught on — and led directly to everything else on this list.