One of my personal favorites is: "I don't give a rat's ass."
which means of course: "I don't care at all."
etymology? I have no idea. But the internets say the following:
The OED gives the first citation of the phrase from the Leon Uris novel, "Battle Cry" in 1953. If it appeared in a novel, there is a good chance the author picked up an expression that had been around for a while before that.
Some suggest that it came from a possibly related phrase "don't give a dead rat" from the incomparable Mark Twain, "The Adventures of Huckleberry Finn" (1884).
Apart from a single occurrence in 1953, Google ngram sees it picking up from 1970, after sporadic use in the 60’s.
Somebody even made a cool graph showing the popularity of the phrases "rat's ass" and "give a rat's ass":
From this graph however, comes the disturbing news that usage of my favorite idiom is now in decline. So tomorrow, I urge you all to try to reverse that trend, and please tell somebody that really deserves to hear it, that you sincerely, and honestly, just don't give a rat's ass.