There are basically two kinds of chips on the market: The kind that hook up to the intake air temperature sensor are not real chips; they are simply passive devices which richen up the air fuel mixture; regardless of whather the engine is running too rich, too lean, or just right. These devices cost $70 to $100; and are typically made from parts which cost $5 or less.
The other kind of chips are really chips (meaning the case contains integrated solid state electronic circuits which are used to modify the sensor inputs to the computer). These devices do far more than change the fuel mixture; they can adjust the spark timing, change the automatic transmission shift points and shift firmness; and vary the fuel mixture to improve either performance or economy; depending on engine speed and load. This kind of chip is individually developed through extensive dynamometer testing for each model of vehicle; does NOT connect to the intake air temperature sensor, and is either made to be plugged into the computer to replace the EPROM chip; or connected to the computer wiring harness through at least 8 wires. These chips are not made to fit most cars; and typically cost $200 or more. They are not advertised on the Internet, are usually sold by reputable performance equipment shops; and come in different models for use on vehicles which have been heavily modified, or for use on largely stock motors.
There are also "piggy back engine controllers" which connect to the computer wiring harness; and contain various controls for use to customize the effects for specific engines or for a variety of operating environments. These cost more than the plug in chips; but are more versatile. Some even contain switches to turn them on and off.
Some types of performance increasing devices will trigger the "check engine" light on certain vehicles. Most of these devices cannot be used without causing the vehicle to fail smog tests; as the tuning changes which improve performance also increase emissions.
I would expect that the well designed and thoroughly tested models will not damage the computer; but I cannot say that about the fly by night brands.
I also should point out that the popular myth that installing dual exhausts on a vehicle will improve gas mileage is frequently untrue. The results of exhaust modifications depend greatly on the type of mufflers used; whether the location and diameter of the pipes and mufflers is altered, and on any engine modifications which have been made to the vehicle. Many late model cars have very closely calibrated fuel mixture settings; which can be thrown way off by changing the exhaust system. Most emission controlled cars are set with a lean fuel mixture. But reducing the exhaust system restriction will change the fuel mixture; often making it go richer at light load, and leaner at heavy loads. This will reduce fuel economy, and also reduce power (but will make lots of noise that sounds like a race motor to an untrained ear). The right way to install a performance exhaust is to then tune the motor on a dynamometer; in order to correct the fuel mixture all the way through the speed and load range. But that can cost hundreds of dollars more than the exhaust changes did. So this is why most people don't do it.
There is only one company, called Gibson Exhaust Systems, which makes performance exhaust systems that are engineered to not upset the fuel mixture and to consistently improve economy and power throughout the range of speeds and loads. But Gibson products cost more than most; and are designed to work in normal driving, rather than in all out racing conditions. So that doesn't appeal to those who want the fastest and the loudest (and who really don't care whether it messes up their mileage or throttle reponse in normal driving).