84, Charing Cross Road by Helene Hanff
84 Charing Cross Road is the exchange of letters between the author, Helene Hanff and bookseller Frank Doel. There is nothing salacious or ribald about their correspondence. Theirs is the romance of the mind. The book was turned into a play and eventually a fantastic movie, starring Anne Bancroft as Hanff and Anthony Hopkins as Doel.
Love in the Afternoon by Lisa Kleypas
In this M/F romance, Beatrice Hathaway, who loves animals and stands slightly outside society despite her natural friendliness, befriends Captain Phelan through letters. Although she uses another woman's name, he recognizes the content of his true lover through the content of her letters.
The Gentleman's Captain by Cristal Crowley
A M/M novel. Many years earlier, Fitz and William fell out of contact, mostly due to Fitz's choices. When they meet up, they repair their relationship by renewing their correspondence.
Letters abound in Austen. I address Darcy's letter to Elizabeth here.
The famous letter in Persuasion is written quickly by Wentworth when he overhears a conversation between Anne and Captain Harville.
Despite Wentworth's quickness (and some of my own references to email in the linked post), the fact is, email isn't the same. The power of the letters in these romances is their palpable nature, their realness. The lovers can fold them up and put them into wallets, under pillows, behind wall hangings. Elizabeth, for instance, can read and reread Darcy's letter until it becomes creased.
"I printed this out and put it in my trousseau" simply doesn't have the same feel.