Approximately 60 eligible subjects will be enrolled over a 24 month period. 21 subjects will be entered into the first stage of a 2-stage Simon Minimax design. If there are 3 or more responses, 39 additional subjects will be enrolled in Stage 2. The minimum number of responses required to move to the second stage, > 3, were noted after the first 9 patients on treatment, and the study then proceeded towards the goal of accruing 60 total patients. Subjects are permitted to receive supportive care throughout the study including transfusion of blood and blood products, treatment with antibiotics, anti-emetics, anti-diarrheal agents, analgesics, erythropoietin, filgrastim (Neupogen), or bisphosphonates, when appropriate. Subjects should continue treatment on study until objective disease progression is documented according to RECIST or withdrawal from the study for other reasons. Subjects discontinuing treatment with paclitaxel prior to disease progression should continue treatment with pazopanib. Subjects discontinuing both agents prior to progressive disease (PD) will be followed for tumor assessment until PD, or until the initiation of a subsequent anti-cancer therapy in the absence of documented PD, or until death, whichever occurs first. Subjects may continue treatment beyond the time of RECIST-defined progression at the discretion of the investigator if the subject is perceived to be experiencing clinical benefit. Overall survival will be assessed for 2 years from first study treatment.