This is a Phase II single-arm, open-label, clinical trial evaluating the efficacy and safety of pazopanib in combination with paclitaxel as first line therapy for subjects with unresectable Stage III and Stage IV melanoma. Previous cytokine therapy is permitted. Subjects must have measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST). Subjects who are not candidates for curative intent treatments are eligible for this study.