In Franco Moretti's Graphs, Maps, Trees, I find the statistic that, of all British novels published in 1776, seventy one percent were epistolary novels, i.e. novels in the form of letters, mimicking correspondence.
Imagine, if you were a Grub Street writer in 1776, the pressure to produce an epistolary novel! It must have been worse than the pressure nowadays to churn out a young adult zombie book...
For most of the late eighteenth century, the epistolary novel was the dominant literary form -- but it seems the only ones we read today are by Pierre Choderlos de Laclos, and, if you're an academic, Samuel Richardson. (Quick, name five other authors of epistolary novels...)
Richardson I suppose was sort of the Tolkien of this genre -- he popularized the form, then, much later, everybody else got on board...
Two contemporary novels in letters are We Need to Talk About Kevin, by Lionel Shriver, and The White Tiger, by Aravind Adiga. In each case, the correspondence is one-sided, there being no reasonable prospect of a reply. In each case, it's easy to forget the novel is epistolary. The action always feels on-scene; it's just that each chapter begins with some form of "dear x" and ends with some form of "yours, y," There's little attempt to imitate the style of contemporary letter writing, and how could there be, when we no longer write letters? Yet in each case, the silence of the addressee does a tremendous job of increasing the book's emotional resonance: this effect really works for me, for reasons I'll have to contemplate further...