Is it just a mash up of various accents from the places they travel or is it it's own accent? Yarr.
The actor Robert Newton made it popular. He was from Dorset in England. It's called the "West Country accent" Much like how Bella Lugosi made the Dracula "I VANT TO SUCK YOUR BLOOD" popular.
Benerson Little's answer to this question from his pirate AMA. :)