For a very long time some writers have indulged in writing novels in letter format – the epistolary novel, one of the most famous being Dracula. There are many many more, however. See here for an interesting insight.
If this form of fiction is of interest, then you should be intrigued by a series of posts featured in Miriam Drori's blog - the series is 'Letters from Elsewhere'.
Already there's a fascinating collection, all from fictional characters...