As it goes with almost all ancient Greek mythology, the story of King Midas exists in a few different forms. But no matter how many there are, Ovid is still #1 in most people's books. Why? Because Ovid was just that good.
Ovid's collection of mythological poetry, Metamorphoses, was also one of the most widely read books of the entire Middle Ages. How do we know? Because we have mountains of books from that time period that mention it.
Pause for biographical info about Ovid:
Ovid was born in 43 BCE, about 90 miles outside of Rome. He had the good fortune to be born into money, which means he got a high-class education. To his father's irritation, Ovid used his education to write poetry. Here are some of the gems he wrote:
Ovid was exiled from Rome in 8 CE. We don't know for sure why he was exiled—it may or may not have had something to do with his poetry. But he kept writing in exile. Nothing would stop this guy.
So what's up with the Metamorphoses then? In a tiny nutshell, it's a collection of poems written in 15 books, which make up a pseudo-history of the world. It starts with the creation of the universe and ends with the assassination of Gaius Julius Caesar in 44 BCE. It's kind of a big deal.
And the story of King Midas finds its way in there, as part of book 11. If you're into Mr. Gold Touch, you can also find him in the story "Midas Never Learns." (You can probably guess how that one ends.)
If Ovid isn't your cup of tea, you can find a bit about Midas in the works of Homer and the Greek historians, Herodotus and Xenophon. None of these guys actually tell the story, but they give us at least something to chew on.