Vandetanib to Treat Women With Ovarian, Fallopian Tube, or Primary Peritoneal Cancer

Inclusion Criteria: * All patients 18 years and older with biopsy-proven epithelial ovarian, fallopian tube or primary peritoneal cancer that is relapsed or refractory to prior standard platinum-and taxane based therapy will be eligible. * Histopathologic diagnosis must be confirmed in the Laboratory of Pathology (LP), NCI. A block of the primary or later access to recut slides is required. If this is unavailable, a recent resection of a metastatic site is required for entry. * All patients must have measurable disease by NCI RECIST criteria and a sentinel lesion adequate for core biopsy through percutaneous biopsy. * Patients must have a performance status of Eastern Cooperative Oncology Group (ECOG) = 0, 1, or 2. * Patients must have good end organ function: * white blood cells (WBC) greater than 3000/mm(3) * absolute neutrophil count (ANC) greater than 1000/mm(3) * platelets greater than 150,000/mm(3) * serum creatinine less than 1.5 mg/dl * liver function tests (AST and ALT) within 2.5 times the upper limit of normal (ULN) * bilirubin less than 1.5 mg/dl * potassium between 4.0 and ULN (supplementation allowed) * magnesium (Mg) and calcium (Ca) within normal limits (supplementation allowed) * Systolic blood pressure less than 160 mm Hg and diastolic blood pressure less than 100 mm Hg (therapy permitted) * Patients must be at least 4 weeks from previous therapy (chemotherapy, hormonal therapy, and radiation therapy, alternative therapy or investigational agents). Carboplatin, must not have been received for at least 6 weeks prior to enrollment. * Patients must have received no more than 4 prior regimens for the treatment of ovarian cancer. * Patients must have recovered from any toxicity related to prior cancer therapy to NCI grade 1, except for peripheral neuropathy, which must have recovered to grade 2 or better. * Women of childbearing age and potential must agree to use adequate barrier contraception (interaction with oral contraceptives is unknown) prior to study entry, during therapy and for 3 months after completion of therapy. * Patients must be able to give written informed consent. * All eligible patients must be registered by contacting Central Registration personnel by fax at (301) 480-0757 between the hours of 8:30am and 5:00 pm, Monday through Friday. Exclusion Criteria: * Evidence of severe or uncontrolled systemic disease or any concurrent condition which in the investigators opinion makes it undesirable for the patient to participate in the trial or which would jeopardize compliance with the protocol. * Evidence of central nervous system (CNS) involvement (patients with abnormal clinical exam or history will require a head CT or MRI. * History of cardiac disorders including: * Clinically significant cardiac event such as myocardial infarction, New York Heart Association (NYHA) classification of heart disease greater than or equal to 2 within 3 months of entry, or presence of cardiac disease that, in the opinion of the investigator,increases the risk of ventricular arrhythmia. * Uncontrolled arrhythmia (multifocal premature ventricular contractions (PVCs), bigeminy, trigeminy, ventricular tachycardia, or uncontrolled atrial fibrillation) which is symptomatic. * Previous history of medication-induced corrected QT interval (QTc) prolongation requiring discontinuation of that medication. * Congenital long (Q wave, T wave) QT syndrome, or 1st degree relative with unexplained early sudden cardiac death(less than 40 years of age). * Presence of left bundle branch block (LBBB). * QTc, corrected per automated electrocardiogram (ECG) standards, that is unmeasurable, or greater than or equal to 480 msec on screening ECG. If a patient has QTc greater than or equal to 480 msec on screening ECG, the screen ECG may be repeated twice (at least 24 hours apart). The average QTc from the three screening ECGs must be less than 480 msec in order for the patient to be eligible for the study. * Patients requiring any concomitant treatment with medication that may cause QTc prolongation or induce Torsades de Pointes will not be permitted to enter this study unless the agent can safely be changed to one not affecting QTc. * Patients requiring any concomitant treatment with medication that may inhibit (cytochrome p450 3A4) CYP3A4 will not be permitted to begin this study. If it is considered medically safe to discontinue such medication, the patient may become eligible once a sufficient amount of time after the last dose of such medications has elapsed to consider the drug adequately eliminated (at least 5 half lives of the drug). * Patients with active infection will not be eligible, but may become eligible once infection has resolved and they are at least 7 days from completion of antibiotics. * Patients with incomplete wound healing from previous surgery or injury will be ineligible. Patients must be at least 4 weeks from a major surgical procedure. * Women who are actively breast-feeding will be excluded. * Currently active diarrhea that is uncontrolled with medication (e.g. bulk agents or loperamide) that may affect the ability of the patient to absorb the ZD6474. * Previous or current malignancies within the last 5 years, with the exception of cervical carcinoma in situ curatively treated, ductal or lobular carcinoma in situ curatively treated and without ongoing therapeutic intervention. * No concomitant use of complementary or alternative medication or other agents (investigational or anti-cancer agents) will be allowed without approval of a principal investigator (PI) or associate investigator (AI). Every effort will be made to maximize patient safety and minimize changes in chronic medications. * Patients with a history of deep venous thrombosis or pulmonary embolism within the past 3 months or those patients requiring ongoing anticoagulation will be ineligible. * Patients with a history of gastrointestinal (GI) bleed or gross hematuria within the past 30 days will be ineligible.