The NYPD stands for the New York Police Department.
The Amazing Spider-Man
The NYPD is lead by Captain George Stacy, the boss of this department (and also the father of Gwen Stacy) the NYPD are first introduce in the film "The Amazing Spider-Man" after the murder of Uncle Ben, where they visit Aunt May & Peter to give them a description of the murderer through an eye witness sketch.
The police are focused on later in the film where it shows from their perspective, their reaction to New York's first vigilante: "Spider-Man". After Peter decides to go on the hunt to bring his uncle's killer to justice after gaining his spider like powers. The NYPD (George Stacy inparticular) see him as an outlaw terrorizing civilians at night and interfering with the NYPD's strategic technique of clearing crime off the streets of New York.
Peter payed a visit to the NYPD, going straight into Captain George Stacy's office, after realizing that Dr. Curt Connors (his daughter's mentor) was the Lizard and warned him of this. He explained very briefly how he transformed and that he is a danger to everyone and is planning something evil, just before Stacy called security to take him out. After this George asked someone to get everything they have on Curt Connors so that they could investigate whether the information Peter told him was true.
After the Lizard attacked Midtown Science High School; they assisted in the evacuation of the school and helped the students overcome what they saw and check if any students were injured during the situation alongside the help of the F.D.N.Y ambulance.
In a later scene of the film Peter is watching the news where the NYPD is holding a press conference and George Stacy is making a speech, where he announces that he will pay a reward for anyone who will bring Spider-Man in for arrest and get him off the streets.
When Spider-Man was on his way to Oscorp to prevent the Genoli Device from spreading Lizard gas across the city and check Gwen was okay; he was intercepted by the NYPD who shot multiple tazer pellets at him which he dodged until he turned a corner (whilst web swinging) where an NYPD helicopter (which George Stacy was in) hit him with one causing him to fall. Multiple police officers dropped from the chopper and surrounded him forcing him to surrender and one cop handcuffed him, Stacy then removed Spider-Man's mask. Because his Spider-sense was tingling Peter was looking down so that Stacy was yet unable to see his face, Spider-Man then using his super-human speed took out all the officers until he was left with Stacy who threatened to shoot. He turned revealing his face which Stacy recognized as Peter Parker (his daughter's boyfriend) and allowed him to go to Oscorp to stop Lizard and save his daughter. As web-slinged away George told one cop (who managed to recover from the unexpected attack) to hold fire which he disobeyed shooting Spider-Man in the leg.
The NYPD then followed Spider-Man to Oscorp (now on his side) where they made sure the building had been fully evacuated taking (Gwen away in a car) and George arrived at the top of the Oscorp tower to give Spider-Man assistance (in the knowledge he had been shot in the leg) and gave him time to place the reptilian antidote in the genoli device. Which involved blasting Lizard with a hose of liquid nitrogen, using multiple shotgun rounds which soon ran out resulting in his death at the hands of the Lizard.
In the "The Amazing Spider-Man (videogame)" the NYPD appear when Spider-Man breaks Curt Connors out of "Beloit Psychiatric Hospital" on the 2nd level as they just exit the facility and web swing off sight the police cars appear.
Later, through out the game as side missions you must locate other escapees of the Beloit breakout and bring them to the rooftops of buildings with chopper landing pads, where you find a NYPD cop waiting to bring them in, furious at Spider-Man for letting these lunatics out in the first place and even threaten to bring him in too, but don't.
Other types of side missions concerning the NYPD in both of the games includes car chases where you start atop the roof of an NYPD car; and police deadlocks (mob shoot outs against police) where you web onto a NYPD chopper for the mission to start and assist in the shoot out.
In "The Amazing Spider-Man 2 (Videogame)" there is a brief level where you must secure a armoured NYPD van containing evidence from the latest crime scene featuring the villain known as "The Hood".
The Amazing Spider-Man 2
The NYPD appear at the end, having a shoot out with Rhino when he is robbing a bank. They try to stop a young child dressed like Spider-Man run into the middle of it, who is saved by the real Spider-Man which comes as a relief to the NYPD after his five month disappearance.