One of the more popular and long standing theories is the fake moon landing. According to theorists in an attempt to divert people's attention from the unpopular war in Vietnam the United States government faked to moon landings. Some theorists claim that no matter what it is impossible for a human to survive in space regardless of what technology they use.
Theorists like to point out abnormalities they see in photographs of the moon walk. One of the more famous of these is the waving flag. Theorists state that because space is in a vacuum there is no air to create a breeze and when you look at the flag the astronauts are holding it's waving. NASA has put out a message attempting to debunk that theory by claiming the reason the flag looks like it's waving is the inertia built up from the hand of the person holding the flag. Theorists also point to a rock that appears to have a number on it like the set is put together with numbers.