In the 1930's, animator Bob Clampett proposed to Edgar Rice Burroughs that he do an animated John Carter of Mars movie. At the very least this clip survives, though I'm unclear as to whether any other clips are available. In the Boing Boing comments section, posters note that while he was alive, Bob Clampett showed it at the San Diego Comic Con every year, and that it is found as an extra on the "Beany and Cecil" DVD.
SciFi Scanner article, with clip
Poster jackanaples comments on Chris Roberson's blog Roberson's Interminable Ramble: "Incidentally, Charles Edward Pogue (screenwriter on David Cronenberg's THE FLY amongst other films) wrote a screenplay for A PRINCESS OF MARS that ERB's grandson supposedly thought the best adaptation of the master's work ever. I'd read online that Pogue occasionally sells this unmade script to fans at Burroughs cons."
At SciFi Scanner, John Brownleee discusses his concerns about the upcoming Pixar film of A Princess of Mars.
Snarkerati reports that the film, a blend of live action and CGI, is the first of a projected trilogy of John Carter of Mars movies, and is set to be released in 2012.
The editor of ERBzine notes, "I have taken photos of the original storyboards that are still preserved in Danton's Tarzana Archives. These will be featured in future ERB Webzines." He also points out that the birth name of Charlton Heston, born well after the start of the ERB Mars series, was John Charles Carter.