Origination of the Hamburger Sandwich :
My original thought was Hamburg, Germany. Per the second article, this answer seems to be the case. :)
The hamburger received first widespread attention at the 1904 World's Fair in St. Louis, Missouri where it creates a sensation. Most Texans believe the vendor in question was Fletch Davis (1864-1941), also known as "Old Dave" who owned a lunch counter in Athens, Texas. Supposedly Fletch Davis, at his Athens lunch counter, took some raw hamburger steak and placed it on his flat grill and fried it until it was a crisp brown on both sides. Then he placed the browned patty of meat between two thick slices of homemade toast and added a thick slice of raw onion to the top. He offered it as a special to his patrons to see if they would like it.
In 1904 Davis and his wife went to the St. Louis World's Fair either on his own or the townspeople took up a collection to send him (there is no evidence for that claim, however). Whoever paid for the trip, he was there since a reporter for the New York Tribune wrote from the fair of a new sandwich called a hamburger, "the innovation of a food vendor on the pike."
The reporter did not name the vendor but Athens resident Clint Murchison said that his grandfather had strong memories of the sandwich in the 1880s but remembered the innovator only as "Old Dave." Murchison also had a large photograph of the midway at the 1904 fair with "Old Dave's Hamburger Stand" marked apparently by his grandfather. When Davis returned from the fair there were already several cafes in Athens serving the sandwich and he went back to firing pots in the Miller pottery works. Tolbert's investigation proved that "Old Dave" was Fletcher Davis from Athens (Tolbert 1983).
In 1983, Frank X. Tolbert wrote the following in his book Tolbert’s Texas, The Henderson County Hamburger:
"It took me years of sweatneck research before I finally determined, at least in mine and in some other Texas historian’s estimation, that Fletcher Davis (1864-1941), also known as “Old Dave” of Athens, in Henderson County, Texas, invented the hamburger sandwich."
In 1984, a plaque was placed on the Ginger Murchison Building, approximately on Fletch Davis' cafe site.
When it comes to America's favorites, though, two of the most humble sandwiches are at the top of the list. The hamburger leads the pack; entire restaurant chains have been founded on it. Many believe that the hamburger made its first appearance as a sandwich at the world's fair in St. Louis in 1904. Prior, the hamburger was served -- sans bun -- as an entree and was called Hamburger Steak; it was named after the German city of Hamburg.
A close second to the hamburger is the simple bologna sandwich.
According to the web site of one major food service company 2.19 billion sandwiches are consumed each year with their bologna, that translates to 6 million sandwiches a day. That is a lot of bologna.