Most places in the United States have independent government agencies that perform services for particular districts.
These agencies normally collect "property taxes".
These taxes are either proportional to the assessed value of real estate, cars, and/or personal property in the jurisdiction, and/or are a fee per housing unit or lot or square foot of particular
form(s) of real estate.
These agencies typically have elected boards.
For example: School boards Fire districts Irrigation districts Sewer commissions [Potable] water commissions Port authorities
(these often control airports, not just harbors)
Some of these districts have highly restricted legislative power.
For example, school boards oversee school curricula, constrained by state guidelines.
(But they do not control the curricula of private schools and homeschools within their boundaries.)
Some fire districts can prohibit activities or real estate development likely to cause devastating wildfires.
Irrigation districts used to impose rules for receiving water that made it hard to grow certain crops.
Sewer commissions can tax or prohibit new construction.
politics.stackexchange.com/users/4547/Jasper
Some examples include the Sheriff, County Treasurer, Tax Collector/Assessor, District Attorney, District Clerk, County Attorney, County Clerk, County Commissioners and Constables.
I live in Texas and just about
everyone that falls under the state infrastructure is elected.
This includes the structure of county governments.
The current Texas Constitution was written in reaction to Reconstruction following the Civil War and reflected a great mistrust of elected officials.
Here's a list of elected officials in one county in Texas.
As a side note, lots of legislation in Texas is written in the form of Constitutional amendments that must be voted on by the people of the state.
politics.stackexchange.com/users/23745/Karlomanio
"Coroner" is an interesting office.
In modern times, it means a government official whose office temporarily stores dead bodies and performs autopsies.
In many states of the United States, the coroner is elected at the county level.
In many counties, the position is combined with the position of sheriff.
Some websites call it a judicial office.
Wikipedia says that it historically acted as a backup to (or check upon) English county sheriffs, plus had certain responsibilities related to the estates of dead people.
politics.stackexchange.com/users/4547/Jasper
Zeb Towne is the dog catcher of Duxbury, Vermont .
He was last elected in 2018, and is now appointed to the same role by the town board.
Thanks to Jasper for the correction.
politics.stackexchange.com/users/16015/Rupert Morrish
"I wouldn't vote for him for Dog Catcher" is an American turn of phrase that often used to denote that someone distrusts a candidate seeking elected office, they wouldn't vote for him to run a seeemingly apolitical job of catching stray animals.
While the office of Dog Catcher is archaic (Humane Society and Animal Control are more commonly used)
it's also not uncommon for these offices to be voted on in local elections.
It should also be noted that while there are a lot of offices up for election in the United States, the office may have staffers who are hired for the job and will keep their positions even when the boss is voted out.
For example, the office of Sheriff is voted, but his deputies are career law enforcement and will remain on the job even if a Sheriff loses his race.
In the case of elected Coroners, the elected official need not actually cut open and examine the bodies, a career coroner with an MD is usually on staff.
THe elected Coroner will typically be charged with the paper work and administration of the office.
politics.stackexchange.com/users/17668/hszmv
In Massachusetts, the following state officers are elected: Governor, Lieutenant Governor, Attorney General, Secretary of the Commonwealth (often called Secretary of State), State Auditor, and Treasurer.
Cities and towns have many different elected officers.
In my town of Arlington, in addition to the executive officers (a 5-member Select Board) and legislative branch (252 Town Meeting members), we elect a Board of Assessors and School Board.
Treasurer used to be an elected position, but we voted in 2018 to make it an appointed position, beginning when the current Treasurer's term ends in 2020.
There's also an elected county Sheriff.
politics.stackexchange.com/users/13966/Barmar
There are several other elected roles, depending on the specific jurisdiction within the US.
As most of them have already been added in other answers, I will add here just the officials who run the elections themselves, as those are elected positions in some jurisdictions and not on other answers' lists.
Head prosecutors (e.g. district attorney, state attorney general), auditors, and financial controllers are also often elected positions.
Some jurisdictions have also proposed and/or instituted elected positions for certain roles like review of police conduct, openness of government records, etc.
politics.stackexchange.com/users/5822/WBT
This question is as put in the title.  It is general knowledge that legislators, high executive offices, and some judges are elected. But are any other elected government offices?  An example could be a position in an independent agency—part of the executive but whose officials are not constitutional officers—of the federal, or of any state or local governments, that is elected. A non-example would be the chair of a yacht club, which is elected but not part of government.
Are there any elected officials in the U.S. who are not legislators, judges, or constitutional officers?
politics.stackexchange.com
<united-states><election>
politics.stackexchange.com/questions/43925
politics.stackexchange.com/users/27888/holomenicus
Some examples include the Sheriff, County Treasurer, Tax Collector/Assessor, District Attorney, District Clerk, County Attorney, County Clerk, County Commissioners and Constables. In Massachusetts, the following state officers are elected: Governor, Lieutenant Governor, Attorney General, Secretary of the Commonwealth (often called Secretary of State), State Auditor, and Treasurer. The following fall into this category: Sheriff, County Treasurer, Tax Collector/Assessor, District Attorney, District Clerk, County Attorney, County Clerk, County Commissioners, Constables, Governors, Lieutenant Governors, Attorney Generals, Secretaries of the Commonwealth (often called Secretary of State), State Auditors and Treasurers.   
The following fall into this category: Sheriff, County Treasurer, Tax Collector/Assessor, District Attorney, District Clerk, County Attorney, County Clerk, County Commissioners, Constables, Governors, Lieutenant Governors, Attorney Generals, Secretaries of the Commonwealth (often called Secretary of State), State Auditors and Treasurers.   