This phase I study will evaluate the experimental drug Romidepsinin patients with advanced cancer. The study will: 1) determine how well patients tolerate Romidepsin; 2) measure blood levels of Romidepsin during treatment; 3) analyze the cellular and molecular effects of the drug; and 4) determine if Romidepsin can shrink tumors. Romidepsin has been shown to kill cancer cells growing in the laboratory and to shrink tumors in animals with various tumor types. In preliminary studies, several patients with a type of lymphoma and one patient with kidney cancer responded to treatment.