The NYPD cars are vehicles that make multiple appearances in both the games and the films of The Amazing Spider-Man out on the streets of New York.
Appearances in the films
NYPD cars make their first appearance in The Amazing Spider-Man where Spider-Man is web-slinging for the first time around New York before he was called Spider-Man, he was known then simply as the "masked vigilante".
Later in the film, though he goes out in his new spandex suit and is chased by the police cars around the streets after avoided being shot at by a cop on a motorbike.
Appearances in the games
In the first game: The Amazing Spider-Man (video game) 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 at the end of the level the police cars appear with their flashing lights and sirens visible in the distance.
In both games consisting of both the first one and The Amazing Spider-Man 2 (video game) you can free roam around New York and prevent crimes that appear on the map, one of these many types of crimes are car chases, where you start atop the roof of an NYPD car and must web-rush ahead onto the car that they are chasing and take out either one or two criminal passengers and save the hostage who is being kidnapped.
Another crime that features in both games is Police Deadlocks, where NYPD cars are parked for cover from the on-fire of criminals.