This is highly field-dependent. In some fields (e.g. psychology), almost all programs do at least a Skype interview, and the vast majority of candidates do on-site interviews (sometimes trips are paid for, sometimes they aren't). Other fields (e.g. math, econ) rarely do interviews, and instead invite students to come to a visit day once they are admitted (often paid for). If you don't know whether interviews are common in your field, I would suggest finding someone to talk about the interview process: your adviser(s), a current graduate student, or even other applicants are all valuable resources.
Almost every program that does interviews will offer some kind of remote interview for candidates who can't make it. However, I think that the majority of the time your chances of admission will be higher if you go to an on-site interview to meet people in person, though the size of that difference is debatable. Also remember that on-site interviews are valuable for you as well, they give you a chance to evaluate the program and the people there.