Do I have to see The Conjuring as well as Annabelle to understand the plot of The Conjuring 2, or does the movie follow a completely new story?
Please avoid spoilers in the answers.
Annabelle is a prequel/spin-off to The Conjuring.
The Conjuring and The Conjuring 2 are the adventure stories of Ed and Lorraine Warren. There is not any special story link between these movies.
The Conjuring 2 is a completely new story.
Therefore, you can watch The Conjuring 2 without watching first part. However,
If you are interested to know where that doll came from, you can watch Annabelle, but it does not have very much to do with The Conjuring 2.