The Black and White
In the USA -- and I imagine in most places -- employees are only contract-bound to carry out the terms of their contract. If you are not contracted to do a certain task, then you are not legally obligated to do that thing as part of your job.
In short: it depends on the terms of the contract.
The Gray
Of course, no contract outlines every single task a supervisor could ask an employee to do. Discretion is required of all parties.
It is relatively normal for coworkers to occasionally ask for personal favors from each other, such as trading a work shift or helping out with a task at work so another person can leave early. This is a normal part of teamwork, and many places have developed a culture of mutual generosity between coworkers. Must you cover for a coworker's shift? No, but if you do, you build goodwill between you and them, and perhaps you will earn the right to ask for a personal favor in the future.
If a PI is asking a grad teaching assistant (hired to help with a class) to do things related to the PI's research, it's generally frowned upon. It may be acceptable in some circumstances and not in others.
All of this is further complicated by the power dynamics between advisors and grads/postdocs, who depend on their mentors for letters of recommendation. Grads and postdocs may want to help out to garner additional favor.
Two Examples
My own contract to be a graduate teaching assistant (GTAs) for a major US university in 2016 specifies certain (university-wide) requirements and says that departments may impose additional requirements if they don't conflict with the main requirements. It says GTAs may be assigned a faculty supervisor who they report to and who will mentor them as necessary. GTAs were to "complete all duties and responsibilities assigned to them by the appointing department(s)" — departments, not supervisors. I couldn't find any document limiting the cope of those tasks, but it's hard to imagine all tasks would be required. There were documents describing the code of conduct and giving tips about how to navigate power imbalances.
Part of the terms for a postdoctoral scholar position at my university (buried in a referenced document, not the actual contract) included the following (emphasis added):
Duties and responsibilities of a postdoctoral scholar shall consist of
those assigned by the president or the president’s designee, who
may be the principal investigator or supervising faculty member. All duties and responsibilities shall be carried out under the direction of
the president or the president’s designee. Duties and
responsibilities shall be related to the expertise and competence of
the postdoctoral scholar.
In other words, the tasks that the PI assigns the postdoc must be related to their job and cannot include personal requests like picking up kids from school. However, the PI could ask the postdoc to write grants that are related to the postdoc's expertise and competence. I imagine similar language exists for similar contracts, but one would need to carefully study a given contract to be sure.
How to Get Help
If you or someone you know has issues with their advisor asking them to do things they don't think are obligatory or ethical, you might point them towards their university ombudsperson program for some investigation. They can determine for that situation whether the requests are legally obligatory. Many universities offer several other levels of mediation, including free legal counsel, anti-discrimination and anti-harassment policies to protect employees at all levels, and other similar resources.
