The National Park Service Civil War Soldiers and Sailors Database is a searchable database containing all names of soldiers and sailors who were on roll call records during the Civil War, both Union and Confederate. It took several years to get the database fully loaded, and they deserve a round of applause for making this data freely available to the public. There is much more information on their website, including cemeteries, regiment descriptions, Medals of Honor, and records from two civil war prisons.
Another good source for Civil War information is The Civil War Message Board Portal.
