In the US it is up to individual states to manage the voting system for their own states (it is not a function of the Federal Government), so the exact rules vary by state. So there can be no one answer to the question as posed.
For the state of Oklahoma (where I live) this information is essentially a matter of public record, and is available for free from the state. If you need them to give you a hardcopy, they will charge a fee for making that.
Voter registration records include voters' name, address, date of
birth, political affiliation, voter ID number, precinct and voting
history, technology center district, school district and municipality.
Voter registration records do not include full or partial Social
Security numbers, driver's license numbers, telephone numbers, e-mail
addresses or voters' race, color, gender or ethnic origin.
By "voting history", they mean which elections each voter has voted in. They of course have no record of what the person voted for. One can make an educated guess based on their party registration, or by cross-referencing from information about that person in other available databases, but that's just a guess.
I don't believe Oklahoma is doing anything deeply unusual here, so I highly suspect similar info is available to the general public in most other states as well. This is how 3rd-party voter registration challenges and purge efforts are made.