It really depends on the car. In large part, removing the muffler on a forced induction engine may give you 4 or 5 horsepower increase.
Scavenging won’t be affected as a few have said if you are retaining the exhaust system and just replacing the muffler with a straight piece of pipe, back pressure loss will also be minimal as the exhaust system still gives you some back pressure, the notion that it will burn valves is utter nonsense.
Removing any restriction from the exhaust will always give you power gains but really they are just nominal and may move your torque band up higher, turbo charged and supercharged cars would generally see an increase.
There are a few saying that your vehicle will be too noisy and create droning, the reality is that there are more restrictions in an exhaust system than just the muffler, the catalytic converters and resonator do contribute to noise cancellation so the noise may not be as loud as you think.
A well designed exhaust system will allow for good flow without sacrificing noise dampening and risk of a traffic fine.