Admissions to PhD programs almost always come with financial support. You should be concerned if you receive an offer of admission that does not include support, as this may indicate a lack of institutional stability or investment in graduate programs.
Admissions to MS programs typically do not come with financial support. There is no guarantee that you will be offered funding at a later point in time, especially at schools that admit many MS students. However, many institutions have funding opportunities within or beyond the department in which the student is enrolled—for example, working as a teaching assistant or a college residence advisor. This may be hard to arrange before you arrive, but more information may be available once you are on campus.