Voiceover Letter

Bob gets a letter from Alice, and starts to read it out loud. Then, Bob's voice fades and gives way to Alice's, even though she's in a different room/town/timezone, before fading back to Bob at the end. Bonus points if the letter is read while we see where Alice is, or where she was while writing the letter.

Often combined with Dead Man Writing for a Tear Jerker—or at least an attempt at one. More comedic shows may do a Sorry I Left the BGM On style gag: Bob sits reading his letter, while we hear someone reading the message, only for Bob to turn round and ask if he can read his letter in peace, please.

Examples of Voiceover Letter include:

Anime and Manga

There's a case from Yu-Gi-Oh!! when Tea reads Pegasus's diary.
Kiki's Delivery Service, the letter right near the end. Her father begins reading it but it fades out into Kiki's voice.
When Cobra gets Vivi's letter in One Piece, which reveals Crocodile to be the mastermind behind the Alabasta civil war, she begins reading the letter aloud.
In Bleach, Aizen's letter to Momo, which he leaves behind just before his apparent death, is read aloud in his voice.
Used in episode 158 of Ranma ½.

Film

A Sorry I Left the BGM On variant in Top Secret- Nick is reading a letter from his manager, who turns out to be sitting next to him talking through a tiny megaphone.
The Curious Case of Benjamin Button uses this for its frame story (although it's a diary, not a letter).
All the time in You've Got Mail. In her commentary Nora Ephron made it clear that she wanted to get away from the computer screens ASAP, for fear that the audience would get spooked and leave the theater.
Played with in Harry Potter and the Goblet of Fire. Harry reads an article by Rita Skeeter, and we hear her voiceover of what it says. A few sentences in, it pisses him off so much he throws it into the fire, and Rita's voice first tries to cram in as much as possible, and then screams as the article burns.

Live-Action TV

Occurs whenever Lizzie reads a letter in the BBC production of Pride and Prejudice.
Baywatch episode "Baywatch Down Under Part 2". As Jake reads a letter from his ex-wife Clare, we first hear it in his voice, then hers. Bonus points because she's deceased at the time.
On CSI, when Sara leaves, v. unexpectedly, the letter is read in her voice, with shots of her in a taxi, as Grissom reads it. Major Tear Jerker.
Spoofed in an episode of Scrubs where it initially looks like an example of this trope, Dr. Cox sitting reading a letter from J.D. with J.D.'s voiceover, but then the camera zooms out to show J.D. is in fact, right there, reading the letter he wrote out loud over Dr. Cox's shoulder.
This, from Tough Guys Don't Dance."
Lampshaded in the sketch show Exit 57, where Amy Sedaris's voiceover gave way to a hacking smoker's cough during the first sentence of her letter, forcing her to start over.
Spoofed into the ground by The League of Gentlemen, which opens with a character reading a letter from his aunt, the voiceover narrating the contents in an old lady's voice. Then panning to show the old lady next to him reading out loud over his shoulder.

Theatre

Used in The Musical of The Phantom of the Opera, with a letter starting to be read by one of the managers, but then it switches to the Phantom, before ending with the manager again. In The Movie of the The Musical, we see the Phantom illustrating what he's talking about in the letter with a diorama.
Used extensively in the Stephen Sondheim musical Passion.

Video Games

Used in Super Mario 64, Paper Mario, and Super Mario Galaxy for letters read by Princess Peach.
Silent Hill 2 - the letter from Mary serves as Book Ends to the game.
In Tales of Symphonia, Collete's voice is used as the voiceover when Lloyd reads a letter from her.
- In Tales of the Abyss, Luke, after being separated from his friends for around a month late in the game, reads letters from Tear, Anise and Guy, and their voices describe what's been going on in their lives.
In Eternal Darkness, one of Edward's later letters to his granddaughter Alexandra, regarding how she can defeat the Ancient that Pious is summoning, is read aloud in his voice, and this is the only letter in the game that receives this treatment, emphasizing its importance.
Oni has Konoko reading her father's memoirs like this. Specifically, the part that narrates how he met his wife and how he took her life via Mercy Kill.
In Assassin's Creed II all important letters are read like this.

Web Original

In a recent Rooster Teeth short, Kerry the intern is ordered by Gus to mow the lawn on the company campus with a push mower (When Kerry asks why he can't use a motorized mower like normal people have since thier invention, Gus yells at him about the price of gas before walking away). As Kerry attempts to mow, he stumbles across a box labeled "Gus' Time Caspule" or something along those lines. He finds some random things inside including a letter, which he begins to read. The letter is read and narrated in Gus' voice, getting progressively creepier and stalkerlike towards Kerry until at the end, where Gus is shown to be reading the letter out loud over Kerry's shoulder with his shirt off.

Western Animation

Spoofed in the animated Aladdin TV series. The letter from Genie is being "read" in his voice, but then we cut to the other side of the shot and see that the letter is actually a mouth reading out loud.
The animated version of The Red Sea Sharks.
The Simpsons also does the parody version, complete with Lampshade Hanging from Homer:

Homer: "So that wasnt just a poignant voice in my head!"

Parodied in an episode of Chowder when Chowder runs away from home, Mung finds his note, after the letter ends he says "It's a good thing there was a voiceover, because his handwriting is terrible", the screen then pans over to the letter which is just a bunch of scribbles.