The purpose of this study is to determine the maximum tolerated dose (MTD) of E7974 administered as an intravenous bolus dose on Days 1, 8, and 15 of a 28-day cycle (Arm A) or on Days 1 and 8 of a 21-day cycle (Arm B) to patients with solid tumors that have progressed following effective therapy or for which no effective therapy exists.