For example the photo on the right is a movie still from the Elvis movie "Tickle Me", during which Elvis briefly teaches an archery lesson.
But much better examples of old archery movies are films like:
The Flame and the Arrow - starring Burt Lancaster (who is frankly awesome in everything he does).
A Man Called Horse - starring Irish actor Richard Harris, whom you may recognize from his many other movies - including playing Dumbledore in the first 2 Harry Potter movies.
Deliverance - starring Burt Reynolds and Jon Voight (I don't care for Voight, but Burt Reynolds is again very awesome. What is it with actors named Burt being so awesome???)
Below is the movie trailer for Deliverance.
And of course there is also films like Rambo II, Rambo III and all the various Robin Hood films...
Robin Hood - 1938, starring Errol Flynn (with archery stunts by Howard Hill).
Robin Hood Prince of Thieves - 1991, starring Kevin Costner.
Robin Hood - 1973, Disney animated film.
Those are three of the more famous ones.
But there is actually many more Robin Hood films...
Robin Hood - 2010 with Russell Crowe
Robin Hood - 1991 with Patrick Bergin and Uma Thurman
Robin and Marian - 1976
Robin Hood Men in Tights - 1993
The Story of Robin Hood and his Merrie Men - 1952, Disney live action
The Men of Sherwood Forest - 1954
Rabbit Hood - 1949 with Bugs Bunny
Beyond Sherwood Forest - 2009
And a slew of other Robin Hood films...
During my research I have determined there hasn't been a lot of William Tell movies made (a planned one for 2012 starring Brendan Fraser was scrapped when the producers ran into financial difficulties getting funding for their film).
There is an old Austrian William Tell movie from 1960, in German of course. Good luck finding an English dubbed version.
And an older William Tell film from 1949 - and a 1998 TV series called "The Legend of William Tell" with 15 episodes (which looks gawd awful, like a cheap rip off of Xena Warrior Princess).
During my research I have determined there was a lot of archery films (especially Robin Hood or Robin Hood esque films) made during the 1940s and 1950s. It was part of an archery fad that started with enormous financial success of the Errol Flynn / Howard Hill film in 1938, and the fad continued until the early 1970s and included the 1972 film Deliverance starring Burt Reynolds.
There was a brief renewed interest in archery in the 1980s when 2nd and 3rd Rambo movies came out, and again in 1991 with Robin Hood Prince of Thieves - but it was nothing like the fad from 1940s to 1970s.
With the introduction of the Lord of the Rings trilogy in 2001 archery saw a bit of interest, but the fast shooting abilities of Legolas made archery look beyond the skill of the common man.
A couple years later however something interesting happened.
Alabama, at that point the fattest state in the USA, was trying to come to grips with an obesity epidemic and high schools were looking for ways to get teenagers outside and exercising. So someone came up with the idea of starting an archery club in one of the schools. The club took off in popularity, the model was spread to other schools in Alabama, and eventually the program was expanded to other states.
By the time films like the Hunger Games, Brave, The Avengers, Killing Season, Hanna and other archery films came out archery was already a growing phenomenon in the USA.
And when those films became popular it was partially because archery was growing as a fad. It was the fad fueling the films, not the other way around. (Although at this point it is more cyclical, archery fanatics are fueling the films and the films are creating new archery fanatics.)
Below is the movie trailer for Killing Season, starring Robert De Niro and John Travolta.