What effect does a Turbo Charger have on the gas mileage of a vehicle, better or worse?

normally worse, since the ECU will match the increased air with increased fuel, so the engine doesn't run lean. But you get a ton more power.

If you're always driving in the higher ends of your tachometer and engine limits, then you will be burning more gas and reducing your mileage. At the same time, the effect of the addition of the turbocharger will add a lot of kick to your car while you're driving around at high rpms.