Need For Speed III: Hot Pursuit (known in Japan as Over Drivin' 3), is the first game in the Need for Speed video game series to feature police chasing down the cracks.
The game also has 4 different game modes: Single Race (where the player can freely choose the car to race and his opponents and also the track he wants), Hot Pursuit (where the player can choose to be the policeman or the fugitive), Tournament (championship with points in a given class), Practice (to be able to practice) and the Knockout modality (where whoever finishes last in the race is automatically eliminated from the tournament).
Good fun.