This is a single-blind (where the participant does not know the treatment he receives), multicenter (study conducted at multiple sites), placebo-controlled (an inactive substance that is compared with the study medication to test whether the study medication has a real effect in clinical study), sequential design (it is a design in a single group of Participants where one or more study medication is administered in a sequence) study to evaluate the potential effects of a single-dose administration of trabectedin on the QT intervals of the electrocardiogram (ECG). Initially, the study will consist of 2 phases: a screening phase (within 21 days before administration of the study medication), and a single-blind treatment phase (for 2 days). Participants who complete the single-blind treatment phase will be opted to take trabectedin in an open-label extension (for a minimum of 6 cycles), as long as they derive a clinical benefit (ie, until there is clear evidence of disease progression or unacceptable toxicity, as judged by the investigator). Participants will be assessed for ECG on predose before the single-blind treatment phase. During the single-blind treatment phase, a placebo control will be given on Day 1, and trabectedin (1.3 mg per square meter) will be administered on Day 2. Participants will be monitored until completion of the 24 hour pharmacokinetic blood sample collection. During the open-label extension (21 days after completion of the single-blind treatment phase), all Participants will receive trabectedin intravenously on Day 1 of each 17- to 49 day treatment cycle. The dose and schedule of trabectedin will be modified according to the type of malignancy being treated (ie, sarcoma, ovarian, or breast cancer). Safety evaluations will include assessment of adverse events, vital signs, physical examination, and clinical laboratory tests which will be performed throughout the study. The study duration for the open-label extension will vary by participant.