The purpose of this study is to find out if the treatment combination of paclitaxel and lovastatin is more effective than the currently available chemotherapy for refractory or relapsed ovarian cancer. This research is being done to improve on currently available chemotherapy for ovarian cancer.

The main goal of the study is to find out if adding lovastatin to paclitaxel increases the number of people whose tumors shrink or whose disease responds to the treatment. Another purpose of the study is to find out how long tumors stay reduced in size before growing again as well as how long people live after receiving paclitaxel and lovastatin. The study will also gather information on the side effects, if any, of this combination of paclitaxel and lovastatin.

Inclusion Criteria:

• Patients with platinum refractory epithelial ovarian cancer: Defined as those patients with histologically confirmed epithelial ovarian cancer that have not responded (progressive or stable disease as a best response) to an initial chemotherapy regimen that included a platinum agent (cisplatin or carboplatin).
• Patients with platinum resistant ovarian cancer: Defined as those patients with histologically confirmed epithelial ovarian cancer that have relapsed less than 6 months after completion of prior platinum based chemotherapy. If the patient had responded but progressed more than 6 months after completing therapy, the patient must have received at least one additional course of platinum containing chemotherapy or recurred within 6 months of discontinuation of the second-line treatment program.
• Measurable Disease: Lesions that can be accurately measured in at least one dimension (longest diameter to be recorded ) as >/= 20 mm with conventional techniques. The same method of assessment and the same technique should be used to characterize each identified and reported lesion at baseline and during follow up. Image based evaluation is preferred to evaluation by clinical examination. Lesions that are considered to be unmeasurable include the following: bone lesions, leptomeningeal disease, ascites and pleural/pericardial disease.
• Prior treatment with any number of chemotherapeutic regimens is permitted as long as there was an interval of at least 4 weeks since the last chemotherapy.
• Prior treatment with paclitaxel chemotherapy is permitted as long as it was administered on a >/= 3 week regimen and it has been at least 4 weeks since the last treatment.
• Normal Hepatic function
• Total Bilirubin < 2 times upper limits of normal range.
• Transaminases < 2 times upper limits of normal range
• Non-pregnant and non-nursing. Treatment under this protocol would expose an unborn child to significant risks. Women of reproductive potential should agree to use an effective means of birth control.

Exclusion Criteria:

• Other serious illnesses, which would limit survival to <2 years, or a psychiatric condition, which would prevent compliance with treatment or informed consent.
• Performance Status >2
• Uncontrolled or severe cardiovascular disease, diabetes, pulmonary disease, or infection, which in the opinion of the treating physician would make this protocol treatment unreasonably hazardous for the patient.
• Patients with a "currently active" second malignancy other than non-melanoma skin cancers. Patients are not considered to have a "currently active" malignancy if they have completed therapy and considered by their physician to be at less than 30% risk of relapse within one year.
• Patients who have received any investigational agent within the prior 4 weeks.
• Age < 18 as there is no safety data for lovastatin in this age range.