In the docks of Portland is a crane where you are supposed to deliver 7 different emergency vehicles. You will get paged when this crane is activated. You will get $1500 for each car you deliver and $200.000 when you have deliverered them all. And you will get pickup icons for all the vehicles as well. The location of the crane is marked on the location map with this icon:

Ambulance
The amulance can be found almost anywhere in Liberty City. They are parked by the hospitals or you can just attack someone or drive over them so the ambulance comes, then steal in right in front of the paramedics.

Police Car
The Police car can be found anywhere in Liberty City.

Fire-Truck
The Firetruck can be found parked outside the fire stations. Or you can just set fire to something and they will come.

Enforcer
This is the police SWAT truck. It can be found parked at the back of the police station on Staunton Island. Use a police car to drive access the gates.

Barracks OL
This is an army version of the Flatbed. You can find one parked at Phil's Army Surplus at the north end of Staunton Island.

Rhino
The Tank. If you have finished all the regular missions, you can find one parked at Phil's Army Surplus at the north end of Staunton Island. Or you can get enough wanted stars to make the army come after you and hijack one from them.

FBI Car
If you get six stars you will have the FBI after you. They drive black Kuruma-type cars with a blue light in the front window. It is very hard to take it from them.