Is there a historical connection between Buddhism and martial arts? Are kung fu monks and all related Hollywood stereotypes based on any actual historical connection between Buddhism and martial arts? Or is it just a fun movie concept? :)
There is a legend that Bodhidharma instructed the monks at the Shaolin Monastery in ways to increase their physical fitness. These exercises later became the Shaolon kung fu.  As one of the documents involved seems to be a forgery, scholars now doubt this connection.

Also see here and here.

Additionally the concept of Do has influenced many japanese martial arts, changing the craft (-jutsu) of fighting to a way (-do) of fighting (e.g. karate-do, ken-do)