It builds sewers, water mains, office buildings, parks, dams, parking garages, electric generators, roads, hospitals, schools, fire stations, etc. Government also sets standards for industrial safety, education, sale of stocks and bonds, building construction, and so forth. Private entities also do all of these things. Even crime and litigation are not the exclusive province of government. Private detectives, security guards and bail bondsmen engage in the same activities as the police.
Arbitration provides a private alternative to the courts.
Yes, there is one defining characteristic that permeates all government activity like a bad gene. That characteristic is coercion. The sole function of government is to force people to do that which they would not do voluntarily, or to force them to refrain from doing that which they would like to do. Anything that people will do voluntarily, does not need government. Whenever we invoke the power of government we are coercing our fellow citizens to do our will rather than their own.