Here is a pretty comprehensive list of just what you're looking for.
It includes etymology on a lot of them, and sources for most.
-EDIT- FOR Kosmonaut
Here is a list of British only slang words for police. :)
Here are a few common, or just awesome, ones from that second link. Some of them contain some etymology.
Bear: Short for "Smokey the Bear" in reference to the hats worn by some U.S. state police being similar to that of "Smokey the Bear". "Bear bait" is a reference to speeders, who may draw the attention of the police and allow slightly slower traffic to exceed the speed limit in their wake. "Bear in the Air" is a reference to a police chopper.
Berry: Originating from blueberry, referring to the blue uniform most officers wear.
Blue Heelers: This is a term used in Australian and is after a breed of dog, the Australian Cattle Dog. This term is use because it accurately describes the personality and appearance (blue uniform) of a police officer. This term became used more frequently as it was used for the Australian police drama series Blue Heelers.
Cop or Copper: While commonly believed to be an acronym for Constable On Patrol, the term refers to "one who captures or snatches". This word first appeared in the early 18th century, and can be matched with the word "cap", which has the same meaning and whose etymology can be traced to the Latin word 'capere'. (The word retains this meaning in other contexts: teenagers "cop a feel" on a date, and they have also been known to "cop an attitude".) Variation: Copper. It is also believed that the term Copper was the original, unshortened word, popularly believed to represent the copper badges American officers used to wear at the time of origin, but in fact probably used in Britain to mean "someone who cops" long before this.
(Name of city)'s Finest: Used in either admiration, or slightly derisive irony, in the United States. In New York City, the term has been adapted to other civil servants, such as "New York's Bravest" (the Fire Department) and "New York's Boldest" (the Department of Correction).
The Gaver: Cockney slang for the police - unknown origin - London.
Mr. Plod, P.C. Plod or Plodder: a British term that arose from the Noddy books by Enid Blyton, in which Mr. Plod was the village policeman. "Plod" has also commonly been used by the British police themselves, as has its (generally disparaging) female equivalent "plonk".
Scum: Used across Britain, as an insult to say that the police are lower than the criminals.
Tyre Biters: A term typically used for country police officers because of their habit of being involved with frequent car chases.
(NOTE: The spelling of this one is a strong indicator that it's British)
Wallopers: Mostly Commonwealth usage, from "wallop" meaning to hit or beat.
Woodentops: British term for uniformed police. Believed to be a reference to the 1950s children's TV series The Woodentops, very rarely in use.
Again, from that second link, and some other external sources, I find these interesting. They are related.
Bluebottle: A British term for policeman that may have derived from Cockney rhyming slang. 'Bottle' is an abbreviation of 'bottle and glass', which is rhyming slang for 'arse'. (See also Bottles).
Bottles: Cockney rhyming slang for Coppers
And my personal favorite, from Wiktionary.com
Cozzer: (slang) a policeman, especially a detective; a rozzer.
Etymology: A mixup of the words "rozzer" and "copper", both slang for british police.
Here are some of the English only one's from the first link, Wikipedia.org
Collar: American and British slang for when an officer catches or apprehends a suspect (collared/having your collar felt). Also used in bravado between officers 'good collar' meaning good arrest or stop.
(Not actually slang for "police officer" but still relevant, I thought.
Constable: A police officer (male or female) in the United Kingdom and many other Commonwealth countries
Ecilop: Australia British for police reversed as seen through rear vision mirror. Motorway (freeway) patrol cars have police written backwards on the front - so it can be read normally in a rear view mirror.
The Gaver or Gavvers: Alternatively Cockney rhyming slang for the police—unknown origin—London, or a Romani language word for the police. (Rom words are used in British English and Cockney.)
Lids: A British term used in the police force to refer to uniformed officers, owing to their distinctive helmets.
Nickers: UK, uncommon British terms, being a pun on "knickers" (female underwear). As the term is spoken not written the silent "k" in knickers is not obvious. Derives from officers "nicking" a suspect, i.e. arresting them, and taking them to "the nick" i.e. the police station.
Rashers: British slang derived from pigs.
Tit-Heads or Tits: Rarely used derogative British term for uniformed police officers originating in the shape of traditional UK police custodian helmet worn by patrolling (male) officers which are or were a similar shape to a large female breast - as in the phrase (to a policeman) "take the tit off your head" meaning "relax" or "imagine you are not on duty".
According to Urban Dictionary:
The Popos: A Police officer. Especially the ones that rides on bikes.
Orgin: California late 80's
Police officers that patrols certain beaches on bikes wore a vest that said PO in huge blockletters on each of their chest which means Police Officer. They usually ride around in group of two's.
When you see them coming by. you see the word "PO" "PO" when they stand next to each other.
I also know of 'bacon' which is a play on the slang pig/piggie. Usually used in the following while being pulled over: "I smell bacon."
Best Answer
I believe that many of these come from the use of French in England amongst the aristocracy after the Norman conquest. Thus 'pork' (porc) is the posh word, 'pig' is the vulgar peasant (or English) word. I don't have any reference for this, but I heard it somewhere in my travels. Correct me if I'm wrong, but it does sound like a convincing story.