There are a lot of crazy people who believe that we never landed on the Moon. Even today, these people exist. Some of them write major Hollywood blockbusters, even!
1977's Capricorn One takes that concept and applies it to a fictional Mars mission. In the movie OJ Simpson and Sam Waterston and James Brolin are to be the first men on Mars, until the government conspiracy forces them to fake the landing. But the plan is too fragile to leave them alive; as they try to escape government hit men, Elliot Gould is a reporter trying to break the story.. while also being hunted. It's one of the great paranoid thrillers of the 70s, and it's got one of the all-time great casts (Hal Holbrook, Karen Black, Telly Savales and Brenda Vaccaro are in there too!). And I think we can have a good argument about where it stands in the Peter Hyams filmography - better than Timecop, maybe better than 2010?
The question, of course, is whether there are people who think our latest Mars mission, Curiosity, is faked as well. I wouldn't be surprised. The rover has already been sending back some AMAZING imagery - click here to check out the latest.