
There is a myth going around that the plans for the Saturn V were deliberately destroyed, usually for some sinister, conspiracy-related reason. Now, in a sense this myth is correct. Once the Apollo program and Skylab were over the contractors simply didn't need the plans, and most were tossed. However, at least one complete set exists on microfilm, in the national archives. Several partial sets - on microfilm or paper - exist elsewhere.
Keep in mind that there was not "a" Saturn V. Each was at least slightly different from all the others, with no true production model. Changes were made as the designers learned from their work, the work of others, and experience. However, the basic design of every Saturn V was the same. And, in fact, had to be, to do the job required of it with the tools available at the time. Any significant change would have resulted in an entirely new vehicle. And there just wasn't time for that, in the hectic days of the race to the Moon.
We could not build a Saturn V today. Or, rather, no competent aerospace effort would try to exactly duplicate the old Saturn V. Manufacturing processes have changed markedly in the past forty years, and the plans would require significant changes to take current methods into account. And if you're going to go to that much effort you might as well start with a clean sheet of paper. We have better computers and materials today, and could produce something with the payload capacity of a Saturn V which would be smaller, cheaper and even more reliable.
There have actually been several proposals in recent years to build what is known as a Big Dumb Booster. So far we simply haven't had anything big enough which needs to be lofted in one piece to justify the effort. (Major parts of the International Space Station are being carried into orbit on large Russian rockets, but even those aren't the largest used in their space program. A modular design makes a lot of sense, though it also makes for less spectacular launches.)
If we do build a Big Dumb Booster, NASA (at least with the current mindset) is exactly the wrong agency for the task. One of the reasons for the success of the Saturn V is that it was only complicated where it needed to be. Everything else was as simple - and as reliable - as a rock crusher. Which is part of the reason every single Saturn V launched successfully delivered its payload to orbit. This includes one Apollo mission where the rocket was hit twice by lightning during the ascent. While the rockets kept running the astronauts reset a few breakers and everything was fine. Note that there were a few launches with problems - such as an engine shutting down early - but the vehicle had enough reserve capacity to compensate.
So here's to the Saturn V. A remarkable piece of equipment which did its job well.