Annabelle is the name of the doll that paranormal investigators Ed and Lorraine Warren kept in their now-closed occult museum. The Warrens claimed that Annabelle was haunted and very dangerous; so much so that it was kept in a locked glass box in the occult museum, with a sign warning people to "positively do not open". Of course, with the various films made in the Conjuring universe over the years, the doll has been thrust into a place in pop culture, even though the movie depiction of Annabelle looks very different from the real thing.
The story of the Annabelle doll allegedly started in 1970, when college student Donna was given a Raggedy Ann doll by her mother. Donna was living in an apartment with her roommate Angie, and both of them were nursing students. Within a few days of the doll arriving in the apartment, however, the two women noticed that the doll seemed to move on its own, even from room to room. The doll was apparently able to write as well, as Donna and Angie kept finding parchment paper - which they claimed they did not keep in the apartment - with messages like "Help Us" and "Help Lou" written in childish handwriting. Finally, Donna came home one night to find that the doll had moved again, and now it had what looked like blood on its hands and chest.
Donna and Angie contacted a spirit medium, who told them that the doll had become the focus of the spirit of a little girl named Annabelle Higgins. Annabelle had died when she was just seven years old, and apparently her spirit wanted to stay with Donna and Angie. Feeling sorry for the little girl's spirit, the two women gave her "permission" to inhabit the doll.
A friend of the two women, Lou, didn't like the Annabelle doll, however; believing it to be evil, he even told Donna to get rid of it. He started to have a recurring dream that Annabelle was strangling him, and on another occasion he claimed that the doll attacked him while he was awake, slashing him and leaving seven claw marks (that healed completely in less than two days and left no evidence, of course). This was enough to convince Donna that "Annabelle" was evil, however, and she got in touch with an Episcopal priest named Father Hagan. Hagan, in turn, felt that he needed more help, and so called in Father Cooke - who called in the Warrens.
The doll, the Warrens explained, was not being possessed by the ghost of a little girl, but by an inhuman, demonic presence - and that presence was looking to move out of the doll and into a human, after which it likely would have harmed or killed everyone in the apartment. After performing an exorcism on the apartment to bring positive energy into it, the Warrens took Annabelle home with them. The doll wasn't done with them, however, as according to the Warrens their car would stall and seemingly try to swerve off the road at every turn and bend in the road, until Ed Warren threw a bottle of holy water on the doll.
Once at the Warrens, Annabelle wasn't immediately put into her infamous glass box. Ed Warren actually kept the doll in his office at first, where she allegedly levitated a few objects and moved around the house, much as she had done in her previous home. One day, however, a priest visited the Warrens and, allegedly, made the mistake of taunting Annabelle. After he left later day, the priest was allegedly nearly killed in a car crash when his brakes failed for no apparent reason. Shortly after that, Ed Warren moved Annabelle into her glass box and put up the sign.
Even this box and the stern warning weren't quite enough to keep Annabelle in check, however. The Warrens told a story of a young couple who visited the museum and began to taunt the doll, tapping the glass and demanding Annabelle do something to them. They were asked to leave the museum; on the way home the man lost control of his motorbike and hit a tree. The man was killed instantly and his girlfriend was hospitalized for over a year. Just like with animals at zoos and pet shops, you shouldn't tap on Annabelle's glass case; but animals are at least unlikely to curse you and try to kill you on your way home from the zoo.
Skeptics argue the Warrens' Occult Museum is full of "Halloween junk, dolls and toys, books you could buy at any bookstore", and honestly, it's very hard to disagree with that. I mean, the Warrens had AD&D books locked up in their museum, claiming they were possessed by evil forces, as well as an LP of Black Sabbath's Paranoid, among many other things. In truth, "Annabelle" is most likely a prime example of the "relationship between pop culture and paranormal folklore" and was influenced by urban legends about haunted dolls, as well as a 1963 episode of The Twilight Zone called "Living Doll":
My name is Talky Tina... and you'd better be nice to me!"
Science writer Sharon A Hill also points out that, regarding the Warrens' stories about Annabelle, "We have nothing but Ed's word for this, and also for the history and origins of the objects in the museum." This is certainly true - in researching this, I could find no corroborating evidence or records about the events and incidents allegedly surrounding Annabelle; just retellings of the story, mostly by supporters of the Warrens. It smacks very much of folklore or an urban legend than of actual, verifiable events.
Sources:
Annabelle (doll) (Wikipedia)
Annabelle (Warrens.net, via Wayback Machine)
"A Night With The Conjuring's Ed and Lorraine Warren" (The Daily Beast)
Living Doll (The Twilight Zone) (Wikipedia)
"The Warrens: Sorting the truth from the Hollywood myth" (The Doubtful News, via Wayback Machine)
"THE PARANORMAL TO POP CULTURE PIPELINE" (Religion Dispatches)