Inclusion Criteria:

1. Patients with any of the following disease categories will be eligible: acute myeloid leukemia (except APL), acute lymphoblastic leukemia, myelodysplastic syndrome, chronic myeloid leukemia in blast phase.
2. Patients must have failed prior therapy with at least one cytotoxic or biologic/targeted agent ( e.g., hypomethylating agents, farnesyl transferase inhibitors, tyrosine kinase inhibitors, thalidomide, etc) for leukemias or MDS, but there is no limit as to the maximum number of prior regimens as long as other inclusion criteria are met. Prior therapies may include bone marrow transplantation. In addition, patients with CML blast phase must have received and failed or be intolerant to imatinib.
3. Age >/= 18 years.
4. Eastern Cooperative Oncology Group (ECOG) performance status 0-2.
5. Patients must have normal organ function as defined below: total bilirubin </= 1.5 mg/dl; alanine aminotransferase (ALT/SGPT) </= 2.5 x institutional upper limit of normal; Creatinine </= 2.0 mg/dl, or creatinine clearance >/= 60 mL/min/1.73m(2) for patients with creatinine levels above 2.0 mg/dl; Cytopenias secondary to multilineage bone marrow failure is acceptable.
6. The effects of BAY 43-9006 on the developing human fetus at the recommended therapeutic dose are unknown. For this reason and because kinase inhibitors 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.
7. Ability to understand and willingness to sign a written informed consent document.
8. In the absence of rapidly progressing disease, the interval from prior treatment to time of study drug administration should be at least 2 weeks for cytotoxic agents or at least 5 half-lives for non-cytotoxic agents. If the patient is on hydrea to control peripheral blood leukemia cell counts, the patient must be off hydrea for at least 24 hours before initiation of treatment. Persistent chronic clinically significant toxicities from prior chemotherapy must not be > grade 1. The use of hydroxyurea is allowed up to 72 hours after the start of therapy with BAY43-9006.

Exclusion Criteria:

1. Patients with APL (unless they have failed therapy with both All-trans retinoic acid (ATRA) and arsenic alone or in combination).
2. Patients with absolute blast count > 20 x 10(9)/L (unless patient has documented FLT3 internal tandem duplication (FLT3/ITD); patients with FLT3 ITD can be included regardless of blast count).
3. Patients may not be receiving any other investigational agents.
4. History of allergic reaction attributed to compounds of similar chemical or biologic composition to BAY 43-9006.
5. Uncontrolled intercurrent illness including, but not limited to, active uncontrolled infection, symptomatic congestive heart failure (i.e., NY Heart Association class 3 or 4), uncontrolled hypertension (i.e., sustained systolic blood pressure >/= 150 or diastolic >/=90), unstable angina pectoris, symptomatic cardiac arrhythmia requiring and not responding to medical intervention, or psychiatric illness/social situations that would limit compliance with study requirements.
6. Pregnant women are excluded from this study because BAY 43-9006 is a kinase inhibitor 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 BAY 43-9006, breastfeeding should be discontinued if the mother is treated with BAY 43-9006.
7. Patients with immune deficiency are at increased risk of lethal infections when treated with marrow-suppressive therapy. Therefore, HIV-positive patients receiving combination anti-retroviral therapy are excluded from the study because of possible pharmacokinetic interactions with BAY 43-9006. Appropriate studies will be undertaken in patients receiving combination anti-retroviral therapy when indicated.
8. Patients who have a donor, are eligible, and have agreed to transplant.
9. Prior therapy with BAY 43-9006.
10. Therapeutic anticoagulation. Prophylactic anticoagulation, (i.e., low-dose warfarin, catheter flushing with heparin) of venous or arterial access devices is allowed.
11. Swallowing dysfunction that impedes oral ingestion of tablets.
12. Evidence of bleeding diathesis (except that explained by low platelets associated with the primary disease).
13. Patients must not be taking the cytochrome P450 enzyme-inducing antiepileptic drugs (phenytoin, carbamazepine, or Phenobarbital), rifampin, or St. Johns Wort.