In the US, yes, almost all programs require tuition and other fees.
In some cases, the student doesn't pay these out of pocket. Instead, the department may pay for them, or they may come out of grant money, and from the student's perspective these will be "waived". However, from the school accountant's perspective they are indeed real fees charged to real entities and paid with real money.
This is considered part of the student's financial support package. Not every school, and not every program, offers the same financial support, so many PhD students do indeed pay fees, sometimes very substantial ones. It may even be that the student receives a salary, and then has to pay tuition out of this salary (although given how silly this is, it tends to be rare).
PhD is kind of a job
In the US, no. It is a studentship, where the student pays the school to train him, not the other way around. The income (or at least lack of expenses) happens by way of financial aid from the institution.
In my humble opinion, this is a very unrealistic mindset, and no serious program would expect students to work for free (or worse, pay to work). However, clearly the establishment is not of this opinion: In many fields, it is in fact considered normal for PhD students to work without pay, and sometimes even being forced to take on loans or side jobs to afford tuition. I suppose they must be getting enough applicants anyways... The point is, in the US, there is no rule saying you won't have to pay fees - this happens to be an excellent thing to discuss during interviews or other stages of the application.