The video of the Apollo 17 lunar module taking off (technically, only the ascent stage takes off) often puzzles people, because the camera tilts up to follow it in flight, implying that someone was there operating the camera, much to the delight of conspiracy nuts. In reality, the lunar rover had a television camera, the Ground-Commanded Television Assembly (GCTA), and it could receive remote control commands from an operator on Earth, which were used to shoot the launch. There are other examples of the GCTA panning and zooming "on its own" when both astronauts are in the frame, away from its controls. It was also used to look around the landing site after the ascent stage has departed.
Another common twist of the claim is that the camera movement in the video appears to have "perfect timing," following the module closely despite the signal delay between the Earth and the Moon. This is easily explained: the take-off time was known in advance and the operators were able to plan ahead, taking into account the signal delay, the camera tilt speed and the angular velocity of the ascent stage. In addition to that, the Apollo 17 clip was the third (and final) try: the first mission to carry the Lunar Rover and the GCTA was Apollo 15, but the camera broke and couldn't tilt up, so it captured only the moment of the launch; on Apollo 16 the camera worked correctly, but the lunar module flew out of the frame due to a miscalculation (the astronauts had parked the lunar rover on the wrong spot). "Third time's the charm," indeed. The camera system operator, Ed Fendell, became briefly famous among space buffs because of his spectacular last-chance success.