The great rings (the three, seven, nine and One) weren't the only ones, you know. There were lesser rings, but we don't really know anything about them. I think it might be that each ring was originally made for a particular person. The elf-rings went to Galadril, Cirdan, and Gil-Galad, the three greatest Elves this side of the sea. The Seven presumably went to various Dwarf kings, since one belonged to the line of kings that were Thorin's ancestors. As for the Nine, it's possible that they were made for nine great Men of the time. We don't really know. At least I don't, maybe the answer is in one of the "History of Middle-Earth" books that I haven't read.