When given a single transfusion, a patient can usually be given blood based on the ABO and +/- part of the Rh groups alone, but there's more to the Rh system than most people know.
As well as the RHD gene, there's also the RHCE gene. The RHD gene can either be present (D, gives you positive blood) or not present (d, gives you negative blood), but the RHCE gene can give you one of four variations of the C, c, E and e antigens. When the two genes combine, you can have any of the following combinations: Dce, DCe, DcE, DCE, dce, dCe, dcE, dCE (which were given simplified names: Ro, R1, R2, Rz, r, r', r", ry respectively).
When patients have to be given regular blood transfusions, especially on a long-term basis, the blood they receive has to be more precisely matched. That's often why there's always a huge push for black donors - because many black people suffer from sickle cell anaemia, for which the treatment is regular blood transfusions, they need blood that better matches their own.