The first book I ever read which was written in letter format was "Daddy Long Legs" by Jean Webster. I was about 12 when I read it and have been hooked on these letter type books ever since. It's about a girl in an orphanage. She has a benefactor who is paying for her education. In return she must write to him regularly.
I just finished reading this last week after seeing (again) the movie with Leslie Caron and Fred Astaire. I actually found the book much more entertaining, but the ending seemed much more rushed than in the film.
Someone mentioned Jane Austen upthread, but not Lady Susan, which is told entirely in letters. Dracula and Frankenstein both use letters and diaries. Wilkie Collins also liked this form, and I can recommend The Woman in White as a great, suspense-filled novel.
One of my lesser-known favorites is E.O. Parrot's The Dogsbody Papers, which traces European history through the documents of the fictional Dogsbody family, including lots of letters. Hilarious!