I don't know what made me think of it, but I couldn't honestly come up with a history for the word "cop". As a verb, I know that it means to steal or snatch, to nab or filch. I was a bit confused as to how it became a noun. From what I can figure based on the collections of several different sites, it originally started out as Scottish slang: caper. Which is, as slang, "a criminal or illegal act, as a burglury or robbery." (Thanks Dictionary.com!) What am I getting at?
Well, when the word entered English, the 'a' was changed to an 'o' (as time passes, languages evolve. At one point the 'a' sounded like our 'o' depending on where you lived.) The word 'cop' evolved from a verb to a noun. Around the 1700's a cop became someone who caught those who stole, snatched, nabbed, or filched. A hundred years later or so, people added (slang) an -er to the end. So a cop became a copper.
Some fun theories that amused me about this were COP stood for Constable on Patrol. Also British cops wore copper buttons... hence the name coppers. Who really knows for sure though?