If you need to find a service number to a member of the US Army in World War II, this National Archives link is very helpful. There is a version of this database on ancestry.com, but their version does not include service numbers for some reason.
Link:
NARA World War II Army Enlistment Records
Edit: When filling in the search form, be sure to follow their guidelines on how to fill in the information, or else you may not find a record that is actually there. Example: In the name field, fill in the name in this format: "SMITH#JOHN#Q"