The Missing Children Incident was an incident occurring at "Freddy Fazbear's Pizza", and is mentioned in both the first and second game.
In the first game, numerous newspaper clippings can occasionally be seen replacing the Rules for Safety sign, normally appearing in the East Hall Corner. These clippings explain that during late June of an unspecified year, a total of five children had gradually gone missing at the pizzeria. Police suspect that a man had dressed up in a costume resembling Freddy Fazbear (possibly even Golden Freddy) and lured the children to a back room where he presumably murdered them.
Soon after the incident, the company's animatronics had begun to leak blood and mucus around the facial areas, and had released a foul odor described by one customer as "reanimated carcasses". This has led to the popular belief that the murdered children were stuffed into the animatronic suits. This incident, along with other incidents and health violations, ultimately led to the closing of the pizzeria, and it was set to shut down by year's end.
The game doesn't confirm whether the man convicted for the incident was actually the murderer, or if kids were stuffed into the animatronics. Since the animatronics attempt to kill other people in a similar manner, some fans believe that the animatronics were the real murderers.
Others believe that it was a homicidal employee (as they would have access to the costumes and the animatronics' AI controls), though the newspaper says nothing as to whether the killer was an employee. Scott Cawthon's hinting of paranormal activity within the pizzeria gave rise to speculation that the ghosts of the five children (and the other victims) might have possessed the animatronics, which caused their macabre behavior. Most fan theories agree that the Purple Man from the Death Minigames is the true murderer involved in this incident, as he is usually present with the imagery of deceased children.
A variation of two certain theories speculates that the murderer may have been a previous night guard, which would explain why the animatronics are so determined to reach Mike Schmidt (and supposedly Phone Guy before him, as heard during Night 4's phone call). Since the killings may have occurred after-hours, this theory raises the possibility that the victims haunting the animatronics want revenge but can only remember for certain that their killer was a night guard (This is leading towards the other theory of where fans believe that the Phone Guy is stuffed into Golden Freddy).
Another theory speculates that the missing children were stuffed into the four animatronics. This would explain the animatronics' foul odor, the leaking blood and mucus, and the parents' comparisons to reanimated corpses. No one knows what happened to the fifth child, though it is theorized that the fifth child may have been stuffed into Golden Freddy. This could explain why Golden Freddy has a little girl's laugh. It is possible that all of the children were killed and disposed of in a more traditional way, though.
Five Nights at Freddy's 2 hints that the previous day shift guard is the one who murdered the children. Phone Guy mentions on Night 5 of the second game that "no one is allowed in or out...especially concerning any...previous employees." This is also possible because Mike worked after both this incident and The Bite of '87 took place, and due to the fact that Jeremy Fitzgeraldis the only protagonist to not be fired from his job as a night guard.
Another candidate could be Fritz Smith, the security guard on the Custom Night that is fired the following day after he tampers with the animatronics (just as Mike was). However, "tampering with the animatronics" could simply allude to the Custom Night gameplay where the player adjusts the A.I. levels of the animatronics. Also, the fact that Fritz worked after previous employees were neither allowed in or out possibly disproves this accusation.
Another theory proposed by the fan base is that Phone Guy is one of the likely candidates who took the missing children. This theory was brought up by MatPat of the famous YouTube theorizing gaming channel, The Game Theorists. The possible connections between The Purple Man and Golden Freddy to the Phone Guy are described; The Purple Man might be a security guard, which Phone Guy was, and The Purple Man's glowing white eyes in the rare "You can't" version of the SAVE THEM death minigame are similar to the ones Golden Freddy has in Five Nights and Freddy's and the player can see "You can't" on the bottom left corner of the death screen from The Purple Man.
Phone Guy also mentions that Foxy was his favorite, giving fans a reason to believe that he was responsible, as in the Foxy Death Minigame, The Purple Man is seen outside Pirate Cove.

