This is a phase II study designed to evaluate the potential clinical efficacy of thalidomide in patients with hormone-refractory prostate cancer. Patients will be randomized to two different treatment arms (low dose versus high dose). An important aspect of this study is to characterize the pharmacokinetics of thalidomide, as well as make correlations between the degree of angiogenesis occurring in a patient and the activity of thalidomide. Each patient that has biopsiable lesions will undergo a pretreatment biopsy of their prostate (or other site of soft tissue disease) and repeat after 2 to 6 months of treatment. Additional information will be obtained on the changes in the circulating levels of the following growth factors: bFGF, TNF, VEGF, and TGFB. Neurological complications are the primary dose-limiting toxicity anticipated with chronic thalidomide administration.