If you steal or hijack a police car you can press Num + or Caps Lock (R3 for the PS2 and X for the X-Box) to activate bonus Vigilante missions. It allows you to chase criminals. You will get a certain amount of time to get the criminal. Just crash into his car until it blows up and if he gets out of the car you can run over him.

This is a great way to get to know the streets which will help you when you do missions or need to get away from the cops. If you catch 120 criminals, 40 in portland, 40 on Staunton Island and 40 on Shoreside Vale, you will unlock two police bribe pickups at you hideout.