Man oh man. You guys were so busy correcting each other you didn't bother to actually watch the movie. Ouch. Okay, here's the straight of it. I've seen this about fifty times, so either I'm insane or I'm right. The line is said by Paul Newman. Strother Martin is The Captain, who doesn't have the mirrored glasses. Those belong to "The Man With No Eyes", as Dragline calls him; the taciturn sharpshooting prison guard. The Captain is a sadistic redneck, with an incredibly annoying voice to boot. After losing himself and laying one down on my boy Luke, he spouts this:

"What we've got here is failure to communicate. Some men you just can't reach. So you get what we had here last week. Which is the way he wants it. Well, he gets it. And I don't like it any more 'n you men."

At the end of the movie/book, Luke says the line again, correcting The Captain's grammar and mocking him:

"Now, what we've got here is a failure to communicate."

Seconds later, he is proven tragically correct. See or read the story; it's fantastic.