The Missouri State Archives holds many military records of Missourians who served between 1812 and World War I. The records are incomplete. The Missouri State Archives is located at 600 West Main, PO Box 1747, Jefferson City, MO 65102; Phone: 573-751-3280.
For veterans after WWI and those from other states, the National Archives and Records Administration (NARA) is the official repository for records of military personnel who have been discharged from the U.S. Air Force, Army, Marine Corps, Navy and Coast Guard. To order military service records, use NATF Form 86. To order military pension records, use NATF Form 85. If you are a veteran or next-of-kin of a deceased veteran, use vetrecs.archives.gov ; all others, use Standard Form 180.
Many records at the National Personel Records Center in St. Louis were destroyed by fire in 1973. For more information about researching military service records, see NARA's Genealogy page.
The above information is from: An Overview of Records at the National Archives Relating to Military Service and the Missouri State Archives web site.The book, Military Service Records at the National Archives will give you an overview of what records are available and the regional branch where they are located.