The epistolary format was extremely popular in the 18th century. Samuel Richardson's novels
Pamela,
Clarissa, and
Sir Charles Grandison were all "a Series of Letters," with the conceit that Richardson was the "editor." There were certainly prose novels being written during this time, as well (Henry Fielding's
Tom Jones, for example).
Les liaisons dangereuses has already been noted in this thread.
After Jane Austen's death, her sister left notes about the composition of Jane's novels. She noted that
Sense and Sensibility was originally written (in the late 18th century, nearly 20 years before it was published) as a novel in letters, and later rewritten in prose. There is a theory that
Pride and Prejudice was also originally a novel in letters (I don't think so; it is just a novel with a lot of letters in it). Of course Austen's novella
Lady Susan is epistolary.
So yeah, it was a thing.
But it became less common throughout the 19th century. Two contemporary epistolary favorites of mine:
84, Charing Cross Road (which was not even fiction) and
The Guernsey Literary and Potato Peel Pie Society.