Like Wales, football pitches and cigarette packets, the Apollo Guidance Computer has become a default analogy. "The asteroid, three times the size of Wales", "If you laid out every sheet of toilet paper used in the Emirates Stadium over the course of 90 minutes, it would cover the same area as three football pitches", "The iPod is about the size of a packet of cigarettes, but even more toxic if burned and inhaled". This morning, I had half an ear on the radio and heard:"this wristwatch has a hundred times the processing power of the computers that guided Apollo".
And that would be how powerful, exactly? There's no one right answer: the Apollo Guidance Computer (AGC) itself was made from around 6000 logic gates, had a 1MHz clock, 1K of RAM and 12K of ROM - and in that sense, it was in the same realm as a ZX81. But much of the mission was based on calculations done by ground-based computers which would have given a ZX Spectrum a run for their money.
It was the first computer to use standard integrated circuits. They cost thousands of dollars apiece at the beginning of the project, tens of dollars by the end. You can't buy those chips today, but you can buy slightly more modern equivalents - which is what John Pultorak did when he rebuilt one in his basement. You don't have to go that far if you want the buzz of being Neil (or to kneel while being Buzz) - there's an online emulator.