Inclusion Criteria:

1. Patients must have histologically or cytologically confirmed relapsed/refractory acute myelogenous leukemia, acute lymphocytic leukemia, myelodysplastic syndrome or blastic phase chronic myelogenous leukemia.
2. Patients that have received cumulative doses (or its equivalent to other anthracycline) of more than 290 mg/m^2 of idarubicin will be excluded from the study. No other limitations in terms of number of prior therapies or type of therapies apply to this study.
3. Patients with blastic phase CML need to have failed imatinib based therapy.
4. Patients must have been off chemotherapy for 2 weeks prior to entering this study and recovered from the toxic effects of that therapy, unless there is evidence of rapidly progressive disease.
5. Use of hydroxyurea for patients with rapidly proliferative disease is allowed but should be stopped 24 hours prior to initiation of therapy.
6. Imatinib mesylate must be stopped 2 weeks prior to entering this study.
7. Other histone deacetylase inhibitors, including valproic acid, should be stopped 2 weeks prior to entering this study.
8. Age > or = to 18 years. Because no dosing or adverse event data are currently available on the use of vorinostat in combination with idarubicin in patients <18 years of age, children are excluded from this study, but will be eligible for future pediatric phase 1 combination trials.
9. ECOG performance status < or = to 2 (Karnofsky >60%).
10. Patients must have normal organ function as defined below: total bilirubin < or = 2 mg/dL, AST(SGOT)/ALT(SGPT) < or = 2.5 X institutional upper limit of normal, creatinine < or = 2 mg/dL, cardiac ejection fraction > or = 50%
11. The effects of vorinostat on the developing human fetus are unknown. For this reason and because HDAC inhibitors as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men 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.
12. Patients with acute promyelocytic leukemia should have received prior therapy containing all-trans retinoic acid (ATRA) and arsenic trioxide.
13. Patients with MDS should have received therapy with either 5-azacytidine or 5-aza-2'-deoxycytidine, unless the patient had a contraindication to such therapy, and should require therapy.
14. Ability to understand and the willingness to sign a written informed consent document.
15. Both men and women of all races and ethnic groups are eligible for this trial.

Exclusion Criteria:

1. Patients may not be receiving any other investigational agents.
2. Patients with clinical evidence of CNS disease should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events.
3. History of allergic reactions attributed to compounds of similar chemical or biologic composition to vorinostat or other agents used in study.
4. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.
5. Pregnant women are excluded from this study because vorinostat is an HDAC inhibitor 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 vorinostat, breastfeeding should be discontinued if the mother is treated with vorinostat. These potential risks may also apply to other agents used in this study.
6. HIV-positive patients receiving combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with vorinostat. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated.
7. Patients who are eligible for potential curative therapy, such allogeneic stem cell transplantation, with or without a more standard induction therapy should be excluded unless they have specifically refused those options.