Diesel vehicle often use turbo chargers. Petrol vehicles frequently do not. What are the advantages and disadvantages of using a turbo charger on a petrol engine?
First: Diesels have a very simple operation which is basically more air, more fuel = more power. On gasoline engines you have to worry more about running too lean, too hot, having incorrect timing. And, you generally already have enough air. You run at higher RPMs and suck in more air. Gasoline is much more volatile than Diesel. It burns very hot! Even most modern diesels now have inter-coolers to deal with the heat. But, with gasoline engines that's a bigger need as the higher exhaust temps are more easily reached. On a diesel it does help with exhaust temps as well, but it's also there just for added power as cooler air = more air. It likely adds less cost, in most cases, to a diesel than it does a gasoline engine because of the lack of additional complications to consider. And you are already paying a premium to get a diesel.
Second: Diesels typically have a more narrow effective power curves over RPMs. The main reason the domestic version of Diesel engines all seem to have a turbo is to help with that shorter power curve. You get 1/4 mile times a lot closer to the gasoline counterpart with no real extra complications other than the engine just has more power.
In Addition: Diesels ignite their fuel from pressure, as opposed to spark. Thus,it makes more sense to add a turbo to increase the volumetric efficiency in order for compression based ignition to occur. When adding additional air to a Diesel you are helping with the ignition process. When you do that on a gasoline engine you are also helping, but that's only a good thing to a point and then you can create knocking (pre-ignition or pinging), timing issues, etc. You are increasing pressure on a platform that isn't designed to run at higher compression like a diesel is. Diesels are designed to run on much higher compression because that is how they ignite their fuel (pressure/not spark). So, adding a little more compressed air won't hurt it. In fact, it helps your fuel burn cleaner and may even increase the life of your engine as less carbon buildup from un-burnt fuel occurs.
In addition to the other reasons mentioned by maplemale, I would add the following:
Cost - Depending on the car, price may be a more important factor for the manufacturer and the buyer than the marginal power gains from a turbo charger. It's not just the parts price that increases, it's also an increase in design cost.
Space - Turbos require plenty of space in the engine bay for all of the additional plumbing.