The Gotham City Police Department (typically abbreviated as GCPD) are the primary body of law enforcement in Gotham City. Unfortunately despite this the GCPD were also almost universally corrupt prior to the arrival of both Batman and James Gordon. Under the leadership of corrupt Commissioner Loeb, the GCPD were little more than thugs with badges. When Batman first appeared the GCPD opposed him not because they viewed him as a dangerous vigilante (though they would use this as a justification) but rather because his actions threatened their criminal activities. In their desperation to kill Batman they also showed a complete willingness to endanger innocent civilians.
Fortunately following the ousting of Commissioner Loeb and James Gordon's replacing him, the GCPD underwent a reform and became much more efficient and honest police officers, albeit ones that also still rely heavily on Batman's assistance.
In the video game Batman Arkham Origins they are again antagonists, this time attempting to collect the reward Black Mask has offered for Batman's head. They are led by Branden in their efforts.
The GCPD is prominently featured in the new TV series Gotham. As with other depictions in the DC Universe prior to Bruce Wayne becoming Batman, the department is rife with corruption and moral ambiguity among its officers, save for one young detective, future GCPD commissioner James Gordon.