Dear Rudolf,
The Library of Congress has online digital records of what is called the WWII honor roll, which is lists of fallen soldiers by state and county. I believe if you go to the Library of Congress Webpage and then do digital search for WWII honor roll you will get a listing. The problem is that you have to look by state and county. It doesn't have the surname search.
There is list of WWII lost though and it will give their serial number I guess and if they were Missing or Killed in action.
These of course are U.S. soldiers.
The state of Missouri has online digital records of WWI Military Service Cards. These would be people that entered the military service from a Missouri location. You might fight a few people from Illinois for example that may have signed up in St. Louis City, perhaps a few from Kansas, near Kansas City, Mo. but the majority of people in this database would be soldiers from Missouri in WWI.
http://www.sos.mo.gov/archives/ww1/Default.asp
Regards,
Barbie