"Pisses me off"!

Anyone have any idea how this very common expression originated?

I don't, but it seems to be a British export. Eric Partridge, Dictionary of Catch Phrases: American and British, from the Sixteenth Century to the Present Day explains "pissed off" as "angry, disgusted, etc., borrowed during WW2 from British troops by American" (part of Partridge's entry for "enough to piss off the Pope").