In the twelfth century knights had a difficult time telling who their opponent were without the use coat of arms on their shields and flags. This tradition of identifying oneself in battle made its way to WWI when the Tricolore cockade of the French Air Force was the first roundel used on combat aircraft. It was a simple design of a bullseye with each ring painted with the French flag colors.
After the French threw that first stone, it was a race for other nations to claim their nations roundel. Since some European countries shared the same color scheme, other nations decided to use a symbol instead. The Germans decided to go with the cross (Eisernes Kreuz) that originated after 1219 when the Kingdom of Jerusalem granted the Teutonic Order the right to combine the Teutonic Black Cross placed above a silver Cross of Jerusalem. So the use of Roundels and the code to which pilots showed respect for their opponents dubbed them the Knights of the Air.
German Empire (Along with Austria and Bulgaria)
Attachment 90372
Though the German roundel changed after 1915, Austria and Bulgaria kept the original design through WWI.
But I did mention that there were countries with the same color scheme. Here is what they were using during WWI
United Kingdom (And Australia and later Canada)
France
Attachment 90360
Italy
Attachment 90361
Poland
Attachment 90381
Romania
Attachment 90362
Russia
Attachment 90363
Serbia
Attachment 90364
Slovenia
Attachment 90365
Spain
Attachment 90366
Thailand
Attachment 90367
Turkey (1918)
Attachment 90368
United Kingdom (Canada and Australia adopted the same RAF markings)
Attachment 90369
United States (American Expeditionary Force 1918-1919 only used in Europe)
Attachment 90370
On May 17th, 1919, The War Department ordered use of national star insignia on all U.S. planes. The new design was (Wargamer's current Avatar):
Attachment 90371
Side note: During WWII, the U.S. decided to drop the red circle in the middle of their roundel because of the Japanese red disc called the rising sun.
For more countries roundels used on aircraft click this Link.