Inclusion Criteria:

* Extracranial germ cell tumor that contains 1 of the following malignant histologies: NOTE: Mixed germ cell tumors that include mature/immature teratoma are eligible provided 1 of the 3 histologies listed above is also present in the tumor.

* Yolk sac tumor
* Embryonal carcinoma
* Choriocarcinoma
* Low-risk disease (closed to accrual as of 01/20/10)

* Stage I gonadal tumors (ovarian and testicular)
* Must have undergone complete surgical and radiologic staging to exclude the possibility of \> stage I disease
* Intermediate-risk disease

* Stage II, III, or IV malignant testicular GCT
* Stage II or III malignant ovarian GCT
* Stage I or II malignant extragonadal GCT
* Previously stage I gonadal patients who have relapsed on the low-risk (observation) stratum of this study(closed to accrual as of 01/20/10)
* Patients with immature teratoma or mature teratoma who relapse with a malignant component
* No patients with any of the following diagnoses:

* Stage IV ovarian and stage III-IV extragonadal GCT
* Intracranial GCT
* Pure mature or immature teratoma, pure dysgerminoma, or seminoma
* Patients with a non-germ cell component in their GCT (e.g., primitive neuroectodermal tumors or rhabdomyosarcoma)
* Alpha-fetoprotein and beta human chorionic gonadotropin tumor markers known

* If \> 5 days have elapsed from the time of obtaining original markers, tumor markers must be repeated before enrollment of low-risk patients and before initiating therapy in intermediate-risk patients (the results of the repeated tumor markers do not have to be known at the time of study enrollment)
* Must be enrolled within 6 weeks of original diagnostic surgery
* Creatinine clearance or radioisotope GFR ≥ 70 mL/min OR a serum creatinine based on age/gender as follows:

* ≤ 0.4 mg/dL (for patients 1 to 5 months of age)
* ≤ 0.5 mg/dL (for patients 6 to 11 months of age)
* ≤ 0.6 mg/dL (for patients 1 year of age)
* ≤ 0.8 mg/dL (for patients 2 to 5 years of age)
* ≤ 1.0 mg/dL (for patients 6 to 9 years of age)
* ≤ 1.2 mg/dL (for patients 10 to 12 years of age)
* ≤ 1.4 mg/dL (for female patients ≥ 13 years of age)
* ≤ 1.5 mg/dL (for male patients 13 to 15 years of age)
* ≤ 1.7 mg/dL (for male patients ≥ 16 years of age)
* No prior chemotherapy
* No prior radiotherapy