This study will evaluate the immunization effects of a vaccine for patients who are at risk for recurrence of their skin cancer. That is, the risk of cancer is higher if melanoma has invaded deep into the skin or lymph nodes. Currently, the only therapy that the U.S. Food and Drug Administration (FDA) has approved for preventing recurrence of melanoma is alpha-interferon. But the research data are controversial. In this study, the vaccine to be used, called gp100, contains a piece of a protein called a peptide, which melanoma cancer cells produce.