Some free online cop games are "Police Emergency," "License for Mayhem" and "Police Train Chase." All of these games are flash-based requiring just a mouse and keyboard.
"Police Emergency" is a fun cop game where the player is a police officer is trying to catch robbers before they take off with the cash. They can use a taser gun on thieves to stop them.
In "License for Mayhem," the player drives a police car through the 12 different levels of the game. They can purchase upgrades for their car and do mayhem throughout the city.
"Police Train Chase" is a game that allows the player to be a police officer trying to chase a train. This train has a thief on it and the cop needs to prevent them from escaping.