There are several reasons why it is good to remove sulfur from crude oil.
First of all, the sulfur present in the crude oil can harm the catalysts that are used in the refining of crude oil into the many useful products obtained from crude oil. Catalysts are materials used to promote chemical reactions without taking part in the reactions themselves. Catalysts are generally very expensive materials and anything that inhibits their activity or shortens their life increases the cost of the refining process.
Second, if sulfur remains in diesel fuel and/or gasoline when it is introduced into a car or truck engine, it will again interfere with the catalytic convertor installed in the exhaust system of the vehicle. The catalytic convertor helps to reduce emissions from the car thus improving air quality.
Third, if sulfur is present in fuel, when the fuel is burned it will be converted to SO2 which is a known precursor to acid rain.