This is a good question. Astronauts have carried personal items into space with them throughout the entire history of the space program, but the procedures associated with and attitudes toward them have undergone significant changes.

On the earliest Mercury flights, personal items were often just zipped into a suit pocket. In July of 1961, Gus Grissom flew aboard Mercury-Redstone 4 carrying a number of items in the left leg pocket of his suit to commemorate the mission. These included several dollar bills, a few small models of the Mercury spacecraft, and two rolls of Mercury dimes. On John Glenn’s famous orbital mission the following year, he carried gold pins depicting the capsule’s flight path around the Earth that he had designed himself and specially ordered from a jeweler. These pins were intended as keepsakes for members of his family and the other original seven astronauts.

But in addition to items that the astronauts personally carried aboard, we have accounts even at this early date of unauthorized items being hidden in the spacecraft in more out-of-the-way places. The Mercury spacecraft were built by McDonnell Aircraft Corporation in St. Louis, Missouri, and a lot of McDonnell engineers had access to the spacecraft before launch, either in St. Louis or during preflight testing at Cape Canaveral. Given this proximity, the temptation to hide an item aboard a spacecraft, retrieve it after the flight, and be able to show one’s friends and family members an item that had actually been in space was understandably attractive. Jerry Roberts, a McDonnell engineer, has stated in an interview that those working the night shift at Cape Canaveral would sometimes curl up dollar bills and lace them into bundles of the spacecraft’s electrical cabling in such a way that they were completely invisible. On some flights, the bills could then be recovered after the mission and the engineers would have their souvenirs. On others, Roberts states that they weren’t able to get post-flight access to the capsule in order to retrieve them, and speculates that those bills could still be folded away inside the relevant spacecraft to this day, in whichever museums they ended up in.

That this practice did indeed take place is again illustrated by Grissom’s Mercury-Redstone 4 mission. Liberty Bell 7, the spacecraft on this flight, famously sank to the bottom of the Atlantic Ocean after the side hatch blew off following splashdown. Thirty-eight years later, the capsule was located at a depth of nearly 3 miles (5 kilometers) and brought to the surface in July of 1999. During the subsequent restoration a number of personal items were found in the interior, including some of Grissom’s Mercury dimes, and – just as Jerry Roberts recounted – several dollar bills inside plastic tubes hidden among the wiring bundles. So these were more than isolated incidents – personal items have been frequently making the trip off the planet since the very beginning, and this continued into the later Gemini and Apollo programs.

Now, the sandwich incident: you mentioned Apollo 16, but you probably mean Gemini 3. I think the confusion lies in the fact that the man responsible, John Young, flew on both of these missions. Gemini 3 was the first manned flight of the Gemini program, and was crewed by Young and Gus Grissom, who was flying his second mission. As part of the evaluation process for the new spacecraft Young was responsible for testing the food items that were available, and decided to play a prank on Grissom with the help of fellow astronaut Wally Schirra. Schirra – himself a great lover of pranks – visited a nearby deli called Wolfie’s in Cocoa Beach, Florida, the night before Gemini 3’s launch. Ordering a corned beef sandwich on rye bread, Schirra kept the sandwich in a refrigerator overnight and then presented it to Young before launch the next morning, who zipped it into one his suit pockets. About two hours into the flight, during his assigned food evaluation activities, Young pulled the sandwich out and offered it to Grissom. Grissom took a bite, but almost immediately had to stow the remainder of the sandwich in his own suit pocket after crumbs started drifting around the cockpit.

The sandwich matter was not commented on further during the mission, but after the flight a combination of engineers concerned about the problems floating crumbs could cause with spacecraft systems, flight surgeons worried about the way an unplanned ingestion of corned beef might have affected their medical data, and reporters recognizing an eye-catching story when they saw one, eventually resulted in a minor controversy. NASA officials had to answer questions in front of a House Committee on Appropriations, and at the end of it astronaut Deke Slayton clarified the official policy on flown personal items in a memo sent to the rest of the Astronaut Office.

Deke Slayton is one of the most important figures of the Apollo program, and is at the heart of this story. He was another of the original seven Mercury astronauts, but didn’t fly in space until 1975 due to a medical condition that grounded him for most of the 1960s. During this period, Slayton instead managed the Astronaut Office and was eventually named Director of Flight Crew Operations, among other things being solely responsible for assigning crews to the Gemini and Apollo missions. In this role, after the Gemini 3 sandwich incident, he made it clear that no personal items that hadn’t been approved by him would be allowed on board the spacecraft during any future mission, although Slayton would later acknowledge in his autobiography that Young had informed him of the sandwich prank ahead of time and that he had allowed it to go ahead.

These informal beginnings and occasional controversies lead us to the heart of your question: the policy on informal personal items flown during the Apollo missions. By the time the first manned Apollo flew in 1968, a policy for crew personal items had been established. Each crew member was provided with an Astronaut Preference Kit (alternately, and hereafter referred to as, a Personal Preference Kit (PPK)). This was a bag with a drawstring top made out of white beta cloth, a fireproof material comprised of silica fibers. It was fairly small, measuring approximately 9 x 6 x 2 inches (23 x 15 x 5 centimeters). Each astronaut would personally pack their PPK with the items they wanted to fly, up to a weight limit of 5.0 pounds (2.3 kilograms). On missions that carried a Lunar Module (LM), each astronaut would also be provided with a PPK that would fly on that vehicle, up to a maximum weight of 0.5 pounds (0.2 kilograms). Even though the LM only accommodated two people, three LM PPKs were provided, so all three crewmembers on an Apollo mission would have a PPK on each vehicle.