The fastest way you can get an Ambulance is to kill some pedestrians and wait for one to come, then steal it. Also, you will find one in front of pretty much any hospital in the game. You can start the Paramedic Odd Job by pushing in the right stick (XBox and Playstation 2) or pressing the 2 Key (PC).
If you get your wanted level to 6 stars, one of these will chase you. There are two locations where you can find one parked, but both of them are in areas where you get wanted levels. The first one is in the Easter Basin Naval Station in San Fierro (5 star wanted level). The other one is in Area 69 in Bone County, on the airstrip (5 star wanted level).
Whenever you get a 4 star wanted level, Enforcers will start coming after you. Also, you may find them sometimes parked in the garage of the police headquarters in the three main cities.
The only way to obtain one of these is to gain a 5 star wanted level, and then steal it from the pursuing FBI, or to steal one from a roadblock.
You can get a Fire Truck anywhere by starting a fire, which will make one come to put it out. Also, one may occasionally spawn in front of Old Codger Antiques in Commerce, Los Santos. You can also find one at the fire station in Doherty, San Fierro, and the fire station between Redsands East and West in Las Venturas.
There isn't any known location where you can find the HPV-1000 parked. However, you can find them patrolling around in the three main cities, so they're very common. Also, if you get your wanted level to 2 stars, you will have them chasing and coming after you. This is one of the better police vehicles to do the Vigilante missions in the beginning of the game.
The standard Police car comes in three different variations, depending on the main city where you encounter them. You can find them patrolling around the streets of the cities, as well as find them parked in front of the stations, although they are usually locked.
The Police Ranger can be found in the police station parking lot in El Quabrados, Las Venturas, when your relationship status is at 50% with Barbara Schternvart. Also, this is the police vehicle that is used whenever you're in the countryside or rural areas.
The Rhino is what comes after you when you get a 6 star wanted level. If you manage to get 100% in the game, one will spawn underneath the bridge near your house in Ganton, Los Santos. There is also one inside Area 69, although you get a 5 star wanted level just for going inside.
The SWAT is an incredibly rare vehicle, as there are two that only appear in the final mission, "End of the Line." The first one is required to get inside the building, which is the one that can be saved in your garage, although it has been known to disappear sometimes after finishing the mission. The other SWAT is inside the building you go into during the mission, but since it's inside, it cannot be saved.