The movie portrays the Annabelle doll as a porcelain doll, but the real Annabelle doll is a large "Raggedy Ann" doll. The Warrens had a special case built for Annabelle inside their Occult Museum, where she resides to this day.
The real Annabelle doll was given to Donna (a college student at the time) by her mother in 1970. She and her roommate Angie noticed that the doll would move subtlety, then within a few weeks became fully mobile moving from one room to another while they were gone.
A 1963 episode of "The Twilight Zone" called "Living Doll" involves a talking doll given to a young girl by her mother. The doll's innocent vocabulary soon takes a sinister tone, especially towards the girl's cruel stepfather. The girl's mother is named Annabelle.
In the film you see two murderers who break in and go on a rampage to kill the neighbors, one of whom was named Sharon. This was no doubt in reference to Sharon Tate, a high-profile victim of a very similar real-life murdering cult led by Charles Manson. This cult, in fact, is mentioned on the news in the beginning of the film the same night the neighbors are murdered.
Unlike The Conjuring (2013) which purports to be based on true events, this prequel is a completely fictional narrative of the previous owner of the doll before it was given to the two nurses shown at the beginning of The Conjuring (2013) (and reprised in this prequel). The only 'theory' as to the origins of Annabelle comes from a medium the nurses hired who claimed that Annabelle Higgins had been a child in the 1860s whose body was found in a field which the house now occupied.
Morganna May, Zach Pappas, and Joseph Bishara are the only actors to return from the previous film. May and Pappas reprise their roles of Debbie and Rick respectively while Bishara, who portrayed Bathsheba in The Conjuring, plays the Demonic Figure in this film.
The characters names 'Mia' and 'John' refer to the lead actors in 'Rosemarie's baby': Mia Farrow and John Cassavetes. This movie is also about a young well to do couple in a luxury apartment having a baby in combination with satanists going for mother and child. The frequent noise of the neighbors in a adjacent apartment is a nod to the same movie.
In one scene in the movie a building shows a large logo with the name "Barclay". Barclay is the last name of the main character Andy Barclay in the popular Chucky horror movie series, in which the plot also revolves around a possessed doll.
The news casts seen on the tv and the cult Annabelle Higgins belong to, 'the disciples of the ram' is evocative of the "satanic panic" that occurred between the late 70's up to the mid-to-late 90's. Where in many social, political, and religious commentators of the era believed that satanic cults were going to effectively take over America. However, like the police officer suggests, they weren't nearly as wide spread as everyone believed they were.
If you look closely, you can see the name Ravens Fair on the box in which the Annabelle doll is inside of. A reference to the film Dead Silence (2007), which featured a town of the same name, which James Wan wrote and directed.
The source of the Annabelle legend actually comes from an episode of The Twilight Zone called Living Doll. Ed and Lorraine Warren likely got the idea from this program. There is even a character in it named Annabelle.
The trivia items below may give away important plot points.
Annabelle (2014) carries references to the cult classic Rosemary's Baby (1968) starring Mia Farrow as Rosemary and John Cassavetes as Guy, a young couple moving into a new building. The leading characters in Annabelle (2014) are Mia and John. They name their newborn daughter Leah; this is the name of one of the neighbors Rosemary and Guy meet in their new building. Both films also incorporate a dramatic scene involving an elevator. Annabelle (2014) is set in 1969, Rosemary's Baby (1968) in 1966. In 1969 actress Sharon Tate was murdered by the Manson Family. She was eight months pregnant at the time. Sharon Tate was married to director Roman Polanski who directed Rosemary's Baby (1968).
When Annabelle is shown being purchased by the woman in the thrift store at the end of the film, the camera pans across the screen to show a Raggedy Ann doll sitting across the room from Annabelle. This is likely an homage to the original Raggedy Ann doll that the film was based on.
The following bit of trivia is inaccurate. The other two dolls from the set are on the shelf, but Annabelle is not. In the scene when the family is about to leave for church, they show the nursery. In the scene the dolls, including Annabelle, are on the shelves. When they return from church, Mia is unpacking the dolls and putting them on the shelf, and comes across Annabelle in the box.