Bites

There have been two instances of a bite in the series, one that killed its victim, and another that didn't.

The Bite
Timeline-wise, the first one was shown in the Night 4 mini-game from Five Nights at Freddy's 4, caused by the bite victim's brother shoving him into the mouth of Fredbear, causing his head to be crushed. This event is never named in-game, but has been referred to as simply "The Bite" in merchandise. The bite victim later died in a hospital, as implied by the flatline sound effect at the end of the Night 5 minigame.

The Bite of '87
This bite is the most mysterious out of the two, as it remains unknown who caused it and who suffered from it. Being first mentioned by Phone Guy in the first game, all that's known is that the bite caused the company to prevent the animatronics from walking around during the day.

Theories
Many people speculate one of the toys to be the culprit of the bite of '87, as the time frame matches. Mangle is the most common choice, due to her amount of teeth and her jumpscare showing her opening her mouth as she reaches the player, which also leads people to believe Jeremy Fitzgerald to have been the one bit.

Trivia

 * One of the lawsuits in Freddy Fazbear's Pizzeria Simulator mentions a bite, it's unknown if that's referring to one of the existing bites, a separate one, or if it's a real one at all.
 * The 8-bit figure displaying the Fredbear bite used to be titled "The Bite of 87", before Scott requested it to be changed.