There has been much speculation about this subject over the years, especially since the advent of the internet and 'cable tv' where people all have equal ability to express their own opinions and to try to convince others.
The main argument of the conspiracy theorists is that the spacecraft used in the apollo missions had less processing power than the most basic of home computers nowadays. This is true, and it would have posed many problems to NASA trying to get a spacecraft to perform all the necessary tasks required to transport the crew safely to the moon and back, but that was a minor task compared to the one they would have faced if the mission was to have been filmed in a studio and made to look real. The fact that NASA did overcome the challenge is a testament to the strength of human endeavour. It is this; the power of human endeavour, that I believe enabled us to overcome the lack of technology and experience needed to put man on the moon in 1969. People who say it was a hoax are insulting the hard work and dedication of NASA and of the 3 astonauts; Neil Armstrong, Edwin 'Buzz' Aldrin and Michael Collins who bravely ventured to unexplored boundaries.
I understand that the conspiracy theorists do have other arguments about the moon-landing, but these are all pie-in-the-sky attempts from people with a lack of basic understanding of physics and technology, trying to disprove one of mankinds greatest acheivements, for what reason, I do not know! Each and everyone of their arguments can be scientifically and without doubt disproven.
Besides, I know "we put a man on the moon!" because R.E.M. said so!