I just finished watching a police series that I recently found. It's called 19-2 and it's a French-Canadian police series based off the Montréal PD. 

You can watch in in a English re-make if you prefer to do so, however I strongly recomend 19-2 with the French actors. Just all around a great series, really loved it. The English re-make is basically exactly the same series however in English, so the plot and story is going to be the same.

 

Sidenote: A season 2 for 19-2 in English is planeed to be released either later this year or the next year. The French-Canadian (Original version) already has 2 seasons but more are comming.

Bad Boys I and II. 

Lethal Weapon movies

Die Hard

Third Watch

Law & Order

Movies: Dirty Harry, Hot Fuzz, Robocop 1 and 3.

TV Shows: Blue Bloods, Chicago PD, Law And Order, Adam-12, Dragnet, Cops, Rookie Blue, Alaska State Troopers, Super Troopers.

Movies: Bad Boys 2, Hot Fuzz, 21 Jump Street(They're cops), Rush Hour 2(They are Detectives)

TV Shows: COPS, Alaska State Troopers, Criminal Minds, K9 Cops

My favourite police shows on tv are southland and ''poliisit'' wich is a finnish police reality show. I dont know if it counts, but i also like ''kommissar rex''. Many of you have propably never heard of it, but it's a fictional cop show filmed in Austria between 1996 and 2004 and in Italy since 2008. The show focuses on 2 to 3 detectives and an german shepherd called Rex.
 
here's some trailers for those who are interested:

 

My favourite show would be Happy Valley (Trailer-