Cop Games

The Dead to Rights games were pretty fun.

Might not be your style, but you should check Puzzle Agent. And you if like point and click games play Sam & Max series.

There's a mod for GTA IV where you play as a cop

'bad pigs 'is nice.

rainbow six splinter cell vegas etc..

Future Cop L.A.P.D

Black Cops II

+1 for Swat 4 & the Rainbow Six games.

The old Blade Runner game is pretty good if you can stomach the graphics.

If you can find it there's actually an "X-Files" adventure game (FMV) where you lead an investigation as a special agent from the FBI, it's pretty great, it was also released on PSX I think.

Another old FMV adventure "noir" game you might find in abandonware was called "The Dame Was Loaded", you play as a private investigator if I remember correctly.

On PSX (available on PC through emulators) Time Crisis & Resident Evil might also remotely fit your description... G-Police also.

On Xbox, Perfect Dark & Golden Eye if you count secret services, there's also No One Lives Forever and all the 007 games.

EDIT: I just remembered there's a bunch of "CSI" games for PC if that counts (from the tv show)...

Still life

In GTA Vice City you are a cop (a moment, to pass the patrouilles)

Future Cop L.A.P.D: Christopher Dorner Edition
Good story. Kinda crispy ending tho.

I'm not sure if these count or not.
F.E.A.R. - You're apart of some special government tactical group.
Puzzle Agent - You're an FBI detective.
Streets of Rage series - Beat em'-up with cops.
Half Life: Blue Shift and Half Life: Opposing Force.
Deus Ex 1
Splinter Cell/Any Tom Clancy games

So yeah, there's my list from my head.. Hope working for goverment organizations is cool too.

Cognition

Indie point and click game about a detective named Erica Reed who has some psychic ability. Only downside is the mouth animations being really awkward/creepy at times.

True Crime was a pretty good one. Similar to GTA except you're a cop.

Dick Tracy on the NES

Sid Meyer's Doughnut Simulator. Best cop game ever made.

There is in fact a mod for GTA IV where you play as a cop. I forget the name of it but it was quite detailed. It looked like a cop simulator, more than anything.

Hopkins FBI? :P old point and clicky game. Was quite enjoyable, good music too

Beyond good and evil

The Shield