J.M. Coetzee's Age of Iron is supposedly a single letter from a dying woman to her daughter.
A novel by Mariama Ba, which is supposedly a letter from a woman to her friend, is actually titled Une si longue lettre ("Such a Long Letter").
Money by Martin Amis is narrated by an ignorant, boorish, drunken (and sometimes amnesiac) slob, John Self, apparently as a suicide note. It's a very long suicide note, and for someone supposedly near illiterate, full of beautiful, if slightly strained, imagery.
Dan Simmons has a fondness of writing parts of his books as journal entries from people who are going insane or dying. It happens part way through Hyperion and near the end of The Terror.
Alphabetized and folder-ized the examples, I took out a few that were either Zero Context Examples or just seemed like straight examples: