public works employees maintain the roads you drive on and plow the snow in winter and collect trash.
...~can be done by private companies
jail/prison guards keep those deemed criminals off of the street when incarcerated.
...~I think some states are moving to contracting this job out also
inspectors check to make sure your food is safe to eat from the grower to the processor to the restaurant that prepares and serves it;
...~buy alot of local foods from local growers, including range beef and chicken and milk...that scales weigh accurately in grocery stores and doctor's offices and ups facilities, and airports; that a gallon of gas from the pump is a gallon.
...~Wow, these make my friends and neighbors that work in these places sound like crooks that have to be kept in line...
investigators respond to complaints re consumer protection laws to make sure consumers receive the protections the law affords them;
...~can be done by private enterprise...maybe even with less corruption? to complaints of abuses allegedly perpetuated by health care providers;
...~abuse by health care providers? not saying it doesn't happen but its an oxymoron for 100% of the health care facilities that I have been associated withto complaints made by seniors re abuses inflicted upon them.
credential reviewers insure that your doctors, nurses, physician assistants, pharmacists, veterinarians, real estate agents, therapists, hair stylists, nail techs, barbers, plumbers, electricians, hearing aid providers, optometrists and opthalmic techs and morticians are properly licensed.
....~more distrust...why are all the honest people working only in the government???
judges adjudicate allegations of criminal and felonius actions and prevent those convicted of same from doing it to you;
...~many lawyers are private entities...I'd hire one of them over a public defender any dayand the judicial system has a staff of public defenders prepared to represent you should you need their service.
....~Who is inspecting their work for accuracy?
clerical support staff administer the recording of your birth and are awaiting the recording of your death; or the payment of your taxes; or the issuance of a motor vehicle license.
....~I'll give you this one, although I think it could be contracted out
the municipal utilities authority insures that your home has potable water for your use and/or a sewer system that works [where appropriate].
....~Live out in the booneys with a well and septic tank...I pay a very nice young man who started his own business to come and clean the septic tank when necessary...he went to school with my middle daughter. I tutored him in math in 5th grade and I like him!
teachers educate your children and the children of the future generation who will be entrusted to take care of you and serve your needs.
...~My kids all went to private schools from kindergarden until graduating from private colleges...Oh, I did homeschool my daughters for 7th and 8th grade since our little catholic grade school only went up to 6th grade. Took the son to a catholic school 16miles away for 7th and 8th grade because he thought he could be a football star 
the transportation and bridge authorities and the faa
....~wouldn't fly if you paid me, Mr. Katz is the only one who has permission to grope me ensure the safety of your travel.
a state banking/insurance dept will make sure that your money is in safe-keeping and that your investment advisor is legally credentialed.
....~again, distrust of local companies? but hey, where were those state people when the banks were forced to make loans to people that could not afford to pay?
an environmental agency will make sure that the air you breath is as safe as it can be.
....~Surely you jest
a state board of public utilities will evaluate a provider's request for a fee increase and determine if it can be granted or modified or denied so that you should not be overcharged.
....~more distrust?
by the way...Mr. Katz reminded me that we have a volunteer fire dept in our township