The goal of this clinical research study is to find the highest tolerable dose of bevacizumab in combination with valproic acid that can be given to patients with advanced cancer that has not responded to standard treatment or where there is no standard treatment for the disease. The safety of this drug combination will also be studied.

Bevacizumab is designed to prevent or slow down the growth of cancer cells by blocking the growth of blood vessels. Valproic acid works the same was way as bevacizumab and is also used in the treatment of seizures, migraine headaches, and mood disturbances in bipolar disorders.

If you are found to be eligible to take part in this study, you will receive the study drugs as an outpatient. You will receive bevacizumab by vein over 90 minutes (for the first infusion) once every 2 weeks. Once the study doctor determines that you are able to tolerate the drug, it will be given over 60 minutes for the second infusion and then over 30 minutes for further infusions. Valproic acid will be given by mouth (capsule(s)) each day for 28 days. You will take valproic acid once or twice a day depending on your dose. Every 28 days is considered 1 cycle.

You will have blood drawn (about 2 teaspoons) and urine collected for routine tests every cycle, about every 1-2 weeks, so that researchers can monitor the safety of the study drugs. Once every 8 weeks you will have tumor markers tested as part of the routine blood draw. You will have a physical exam once a cycle.

You will have either a CT or MRI scan of the tumor about every 8 weeks to check the status (whether it is growing or shrinking) of the cancer. If your doctor thinks other tests are necessary he/she will discuss those with you.

You will continue to receive bevacizumab and valproic acid as long as the disease is considered stable. You will receive up to 12 cycles of the study drug. If the disease gets worse or you experience any intolerable side effects, you will be taken off this study.

You will have an end-of-study visit 28 days after your last dose of bevacizumab. At this visit, you will have a complete physical exam, including measurement of your vital signs and blood pressure. You will have a neurological exam, and blood (about 2 teaspoons) will be drawn for routine and tumor marker tests. You will be asked about any medications you may be taking and whether you have had any side effects. You will also be asked how well you are able to perform daily activities.

This is an investigational study. Bevacizumab and valproic acid are both FDA approved and commercially available. Their use together in this study is investigational and authorized for use in research only. Up to 80 patients will take part in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. Patients with pathologically confirmed malignancy that is metastatic or unresectable and refractory to standard therapy or for whom there is no standard therapy that induces complete remission (CR) of at least 10% or an increased survival of at least 3 months.
2. There is no maximum allowable number of prior chemotherapy regimens, provided all other eligibility criteria are met.
3. ECOG performance status less than 2.
4. Patients must have normal organ and marrow function as defined below: - absolute neutrophil count greater than or equal to 1,000/mcL - platelets greater than 50,000/mcL - total bilirubin less than 2 mg/dl - creatinine less than 2 mg/dl
5. The effects of bevacizumab on the developing human fetus are unknown. For this reason and because valproic acid is known to be teratogenic, women of child-bearing potential and men who may impregnate a woman must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately.
6. Ability to understand and the willingness to sign an MD Anderson IRB approved written informed consent document.
7. Both men and women of all races and ethnic groups are eligible for this trial.

Exclusion Criteria:

1. Patients who have had chemotherapy or radiotherapy within 4 weeks prior to receiving first dose of study drug or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier.Patients may have received palliative radiation immediately before (or during) treatment provided radiation is not to the only target lesion available.
2. Patients may not be receiving any other investigational agents for 28 days prior to first dose of drug on this study, and while pt is receiving this study drug.
3. Patients whose brain mets or primary brain tumor includes symptoms that in the opinion of the principle investigator would either put the patients at unacceptable risk greater than the risk of the underlying cancer or if the treatment would unacceptably confound the analysis of the toxicity assessment.
4. History of allergic reactions attributed to compounds of similar chemical or biologic composition to bevacizumab or valproic acid .
5. Major surgery within the previous four weeks.
6. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, HTN (with 2 or more antihypertensives), unstable angina pectoris or psychiatric illness/social situations that would limit compliance with study requirements.
7. Pregnant women are excluded from this study because valproic acid is an agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with valproic acid and bevacizumab, breastfeeding should be discontinued if the mother is treated with these agents.
8. Patient who are already on antiepileptic agents, for example; phenytoin, valproic acid, and neurontin will be excluded.