Avastin in Combination With Docetaxel in Ovarian/Fallopian Tube/Peritoneum Carcinoma

Inclusion Criteria: * Signed informed consent * Pathologically confirmed epithelial ovarian cancer, peritoneal serous cancer, or fallopian tube cancer * Patient's disease recurrence or progression occurs between 0 to 12 months (1 to 365 days) from prior platinum-containing chemotherapy regimen. Patients, however, may not receive study drug until at least 28 days from prior chemotherapy. * The patient may have received up to three prior chemotherapy regimens for the treatment of this malignancy. Patients who may have received prior treatment with paclitaxel and/or a platinum compound will be allowed. Rechallenge with the same platinum based regimen is considered 1 prior regimen. Patients who have been treated with consolidation treatment are allowed and the consolidation will not be considered a separate regimen. Hormonal therapy (i.e. progesterones, estrogens, anti-estrogens, aromatase inhibitors) will not be considered a prior chemotherapy regimen. * Measurable or evaluable disease either by the Gynecologic Oncology Group (GOG) Response Evaluation Criteria in Solid Tumors (RECIST) or cancer antigen (CA)125 criteria \[Journal of the National Cancer Institute (JNCI), Vol. 96, No. 6, March 17, 2004, Vergote JNCI 2000\] * At least 4 weeks since major surgery, with full recovery * At least 3 weeks since radiotherapy, with full recovery. The measurable disease must be completely outside of the radiation port. * Eastern Cooperative Oncology Group (ECOG) performance status \</= 2 * Hematologic (minimal values): Absolute neutrophil count \>/= 1,500/mm\^3, Hemoglobin \>/= 8.0 g/dL (transfusions allowed), Platelet count \>/= 100,000/mm\^3 * Hepatic: Total Bilirubin \</= upper limit of normal (ULN), alanine transaminase (AST) and alanine transaminase (ALT) and alkaline phosphatase must be within the range allowing for eligibility. In determining eligibility the more abnormal of the 2 values (AST or ALT) should be used. * Women of childbearing potential must have a negative pregnancy test. * Patients of childbearing potential must be willing to consent to using effective contraception while on treatment and for 3 months following the completion of treatment. Exclusion Criteria: Prior treatment with Docetaxel or Avastin * Concurrent immunotherapy or hormonal therapy for the specific purpose of treatment for the ovarian cancer. Any hormonal therapy directed at the malignant tumor must be discontinued at least one week prior to enrollment in order for the patient to be eligible to participate in this trial. Continuation of hormonal replacement therapy is allowed. * Peripheral neuropathy \>/= grade 2 * History of a severe hypersensitivity reaction to Docetaxel, Avastin, or to other drugs formulated with polysorbate (Tween) 80. * Current, recent (within 4 weeks of the first infusion of this study), or planned participation in an experimental drug study of Avastin * Blood pressure of \>150/100 mmHg Unstable angina * New York Heart Association (NYHA) Grade II or greater congestive heart failure * History of myocardial infarction within 6 months prior to Day 1 * History of stroke within 6 months prior to Day 1 * Clinically significant peripheral vascular disease * Evidence of bleeding diathesis or coagulopathy * Presence of central nervous system or brain metastases * Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to Day 0, anticipation of need for major surgical procedure during the course of the study * Minor surgical procedures such as fine needle aspirations or core biopsies within 7 days prior to Day 0 * Pregnant (positive pregnancy test) or lactating * Urine protein: creatinine ratio \>/= 1.0 at screening * History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 6 months prior to Day 0 * Serious, non-healing wound, active ulcer, or untreated bone fracture * Evidence of malignancy in the last 5 years, other than nonmelanoma cutaneous carcinomas * History of hemoptysis (bright red blood of 1/2 teaspoon or more) within last 3 months * Patients believed to possibly be at higher than average risk of perforation will be excluded from study. This includes symptoms or findings of partial or complete bowel obstruction, history of fistula, patients requiring parenteral nutrition and hydration, and those with history of prior perforation due to tumor or perforation within last 6 months from other causes. * Inability to comply with study and/or follow-up procedures. * Patients who are not on a stable dose of anticoagulation therapy. Patients who are on a stable anticoagulation regimen, including coumadin or low molecular-weight heparin, will not be excluded.