There are several of them; wiki has a list of Fi-103 on display, although it does not list the one on display at the US's National Air and Space Museum with a more extensive list of survivors. The Imperial War Museum has a V-1 alongside a V-2 as well as a launch ramp . For reading materials, I suggest Steven Zaloga's V-1 Flying Bomb 1942–52: Hitler’s infamous "doodlebug” as a starting point and his annotated bibliography will be a good launching pad for further reading.

There are surviving V1 casings displayed in the RAF Museum at Hendon and the Imperial War Museums at London and Duxford. Duxford has a launch rail as well. It seems probable that there are survivors elsewhere in the world.