Did people sit in the back of Greek comedies, scribbling the lines down to perform it later on the cheap? Were people cranking out typo-ridden King James bibles on printing presses in their basements?
I can't imagine the urge to obtain media or entertainment for cheaper than the normal price is new, but where did it start?
In order for the crime of media-piracy to exist you need to have a law that establishes the rights of media ownership (some form of copyright law) If you don't have a concept of ownership around something then you can't have the concept of stealing it.
Wikipedia's page on the history of copy right law references a 6th c AD dispute in Ireland over the rights to reproduce a religious text which resulted in King Diarmait Mac Cerbhaill giving the judgement
"To every cow belongs her calf, therefore to every book belongs its copy."
Which is essentially the same meaning as the modern
'the author asserts the moral right to be identified as the author of this book' in reprints.