John,
It was possible to buy versions of popular diesel engined cars without a turbocharger, the previous generation VW Golf SDI was a popular example. Fuel consumption was good, but the engine was a bit limited in power and torque.
The turbocharger fitted to most modern diesel engined cars, for example the Golf TDI, is there to increase the amount of air in the combustion chamber.
More air, means more oxygen, and this allows the engine to burn more fuel, and extract more power and torque from the same sized engine.
Under normal road conditions, people often report equal or better fuel consumption from a turbocharged car, compared to non-turbocharged, and much better driveability.
Why do you see some cars sporting the name Turbo, some using the name CDI, some Pumpe Deuse? It's mainly product marketing, ten or so years ago Turbos were starting to appear on diesel cars, so that got slapped on the back of the car.
Robert