I started watching Brooklyn 99, a show about police detectives. They started debating over what the best cop movie is. Made me think. What is your favorite? Die Hard, Speed (I almost put Speed 2 in as a joke), Hot Fuzz, Lethal Weapon? This list goes on and on. It seems to be a genre they don't seem to make a whole lot of these days.
Dirty Harry - from the beginning to the end Harry Callahan is depicted as a cop who is dedicated to catching bad guys and doing whatever it takes to do so.
Colors - perhaps the first theatrical look at LA gangs in the 1980s.
The Naked Gun - This movie was funny but like most silly cops, Frank Drebin eventually solves the crime. Lots of memorable scenes and jokes. Getting Leslie Neilsen, Pricilla Presley, Ricardo Montalban, OJ Simpson, George Kennedy and even Reggie Jackson in the same movie was brilliant. The sequels were pretty good too.
Die Hard - not sure if this is the best cop movie, but it is a pretty great Christmas movie. The movie made Bruce Willis a big movie star and really defined the new era of action movie.
Beverly Hills Cop - for the record, this was the first R rated movie I saw with my parents in a movie theater. Eddie Murphy at his best, delivering jokes and physical action.
Chinatown - Jack Nicholson in one of his best early roles.
Heat - The first movie starring Pacino and DeNiro, although they did not have many scenes together. The bank shootout is one of the best shootouts in movie history.
Silence of the Lambs - technically Clarice Starling is a cop - edge of your seat movie the whole way through and the finest performance from Anthony Hopkins
Witness - early in Harrison Ford's 1980s dominance this movie was a departure from the typical murder mystery and really a great blend of action and suspense
The Untouchables - a really good depiction of the hunt for Al Capone with Costner, Connery and DeNiro. Brian Depalma has some great crime movies, this one focused on the good guys.