This study will evaluate the effect of a treatment using the two drugs, pazopanib and bevacizumab in an alternating fashion. The purpose of alternating (taking one drug and then the other) treatment with these two drugs is to try and prevent your cancer from developing a resistance to these drugs. Pazopanib will be taken by mouth at home and bevacizumab will be administered by intravenous infusion in the clinic. (Intravenous infusion is through a tube inserted by needle in a vein in your arm). This is a combined phase I and phase II study. The phase I part of this study is to determine the highest safe dose for use in phase II. Once the highest safe dose of the two drug treatment is found the phase II study will begin. The purpose of this study is to find out what effects (good and bad) pazopanib and bevacizumab will have in patients with your type of advanced kidney cancer. We will also perform blood studies to determine how this treatment is affecting your cancer. These studies will look to see: how many growth factor cells (cells that help cancer progress), how many immune related cells (cells that effect your immune system) and how much of the drug pazopanib is in your blood.