"Downfall" is the lead single from the 2002 album "The Lonely Position of Neutral" by rock band Trust Company.
"Downfall" is the name of 2004 German movie about the last days of Adolf Hitler. A particular scene in the movie as spawned a "Hitler Reacts" meme. Far more people have probably seen some version of that meme than have seen or even heard of the movie.
Downfall was the codename for the planned invasion of Japan in World War 2. It consisted of the invasion of Kyushu in fall 1945 (Operation Olympic) and an invasion of Honshu in spring 1946 to seize Tokyo (Operation Coronet). Planning for Downfall was never completed and the operation was never carried out due to Japan's surrender in August 1945 after the atomic bombings of Hiroshima and Nagasaki and the Soviet entry into the war. The likely results of Downfall (had the war not ended) remain a point of debate, particularly because the various casualty estimates that form part of the lasting controversy regarding the use of atomic bombs. For more information I recommend "Downfall: The End of the Imperial Japanese Empire" and "Hell to Pay: Operation Downfall and the Invasion of Japan, 1945-1947" by D.M. Giangreco.