Docetaxel, Thalidomide, Prednisone, and Bevacizumab to Treat Metastatic Prostate Cancer

* INCLUSION CRITERIA: Androgen-independent metastatic adenocarcinoma of the prostate defined as progressive metastatic disease while on gonadotropin releasing hormone (GnRH) agonists or post surgical castration Histopathological documentation of prostate cancer confirmed in the National Cancer Institute (NCI) Laboratory of Pathology at the National Institutes of Health, the Pathology Department at Walter Reed Medical Center or the Pathology Department at National Naval Medical Center, prior to starting this study. In addition, patients whose slides are lost or unavailable will be eligible for the study if they provide documentation of prostate cancer and if they meet criteria of clinically progressive prostate cancer as outlined in section 3.1.1.3. Clinically progressive prostate cancer documented prior to entry. Progression must be documented by at least one of the following parameters: * Two consecutively rising prostate-specific antigen (PSA) levels. The first rising PSA must be a minimum of one week from a reference value. It is recognized that PSA fluctuations are such that the confirmatory PSA value might be less than the previous one. In these cases, that patient would still be eligible provided the next PSA was greater than the first rising PSA value. Patients must have PSA greater than or equal to 5.0. * At least one new lesion on bone scan. * Progressive measurable disease. Patients must have undergone bilateral surgical castration or must continue on GNRH agonist. Those patients receiving an anti-androgen agent and are entering the trial due to a rise in PSA must demonstrate a continued rise in PSA 4 weeks after stopping flutamide and 6 weeks after stopping bicalutamide or nilutamide. Patients may not have received any chemotherapy for metastatic prostate cancer Age greater than or equal to 18 years Eastern Cooperative Oncology Group (ECOG) performance status less than or equal to 2 Life expectancy of greater than 3 months Patients must have adequate organ and marrow function as defined below: Leukocytes- greater than or equal to 3,000/microliter Absolute neutrophil count- greater than or equal to 1,500/microliter Platelets- greater than or equal to 100,000/microliter Hemoglobin- greater than or equal to 8.0g/L - transfusions acceptable Total bilirubin- less than or equal to 1.5 times the institutional upper limits of normal Aspartate aminotransferase (AST)serum glutamic oxaloacetic transaminase(SGOT) and alanine aminotransferase (ALT)serum glutamic pyruvic transaminase(SGPT) - less than or equal to 2.5 times the institutional upper limits of normal Creatinine or Creatinine clearance- less than or equal to 1.5 times the institutional upper limits of normal or greater than or equal to 40 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal. Recovered from any toxicity from surgery or radiotherapy Must be willing to travel from their home to the National Institutes of Health (NIH) for follow-up visits Able and willing to follow instructions and conform to protocol. Patients may have had no other active malignancy within the past 2 years with the exception of non-melanoma skin cancer and superficial bladder carcinoma No history of myocardial infarction within the past 6 months, uncontrolled congestive heart failure (CHF) or uncontrolled angina pectoris Patients must agree to use adequate contraception (abstinence; hormonal or barrier method of birth control) for the study and at least 2 months after completion. Ability to understand and the willingness to sign a written informed consent document. EXCLUSION CRITERIA: Present clinical signs or symptoms of brain and/or leptomeningeal metastases confirmed by computed tomography (CT) or magnetic resonance imaging (MRI) brain scan. Uncontrolled, intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure (American Heart Association (AHA) Class II or worse), unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements Persistent systolic blood pressure greater than or equal to 170 mmHg or diastolic blood pressure greater than or equal to 100 mmHg. Human immunodeficiency virus (HIV)-positive patients receiving combination anti-retroviral therapy are excluded from the study because of possible pharmacokinetic interactions with docetaxel, bevacizumab, and/or the combination. Proteinuria, as demonstrated by a urine, protein, creatinine (UPC) ratio greater than or equal to 1.0 at screening, required to be assessed if urine dipstick is greater than or equal to 1+. Urine protein should be screened by urine analysis for Urine Protein Creatinine (UPC) ratio. For UPC ratio \> 0.5, 24-hour urine protein should be obtained and the level should be \< 1000 mg for patient enrollment. Note: UPC ratio of spot urine is an estimation of the 24 urine protein excretion - a UPC ratio of 1 is roughly equivalent to a 24-hour urine protein of 1 gm. UPC ratio is calculated using one of the following formula: * \[urine protein\]/\[urine creatinine\] - if both protein and creatinine are reported in mg/dL * \[(urine protein) x 0.088\]/\[urine creatinine\] - if urine creatinine is reported in mmol/L Therapeutic anticoagulation with coumadin, heparins, or heparinoids. Greater than Grade 2 peripheral neuropathy at baseline. History of transient ischemic attacks (TIA) or cerebrovascular accident (CVA) within the past 2 years. History of allergic reaction to docetaxel, prednisone, thalidomide and/or bevacizumab or related products. Patients who are on concurrent investigational agent(s) Patients who are unable to ingest oral medication. INCLUSION OF WOMEN AND MINORITIES Men of all races and ethnic groups are eligible for this trial. Every effort will be made to recruit minorities in this study. Women are ineligible for this study.