Bags of Letters

The protagonist is at a crucial turning point in their life and things are generally looking pretty grim. Rather suddenly, the character is surrounded with bags and bags of letters. While the letters are written by people who aren't even in the story, the sheer quantity of envelopes implies that they accurately represent public opinion, constitute valid legal arguments, or create some other opportunity for the character they are addressed to.

Bags of Letters can be a Smoking Gun. If a few letters are read aloud, the bag will often turn out to be full of Strongly Worded Letters. But the important thing is quantity. The trope is a sort of analog equivalent of The Switchboard is Lighting Up where a character pulls some kind of outrageous stunt on live radio or television and is about to be kicked off the air when suddenly hundreds of people start calling in, presumably saving the person.

Sometimes, the letters aren't even read or opened, like in Miracle on 34th Street. Other times, a character will read a few aloud and the audience is left to assume that the entire bag of letters sounds like the few they looked at like in Mr. Smith Goes to Washington.

The mass of letters often appear on camera in literal bags although many movies use the trope to refer to letters offscreen or just show a pile of letters which were presumably in a bag at some earlier point.

This trope is a form of Deus Ex Machina since most of the letters are written by characters who aren't even in the story. The effect is usually positive, but the letters can occasionally have a negative effect on the protagonist.

Examples of Bags of Letters include:

Film

In Miracle on 34th Street, at the end of the famous courtroom scene, bags and bags of letters addressed to Kris Kringle are brought into the courtroom until they are piled high enough to block out the judge. While the prosecutor argues a few letters delivered by the USPS don't constitute a valid legal defense, the bags and bags of letters do constitute a valid legal argument.
In Mr. Smith Goes to Washington, Mr. Smith expects his filibuster to sway public opinion in his favor, but he is presented with bags of letters that reveal public opinion has turned against him. The mass of letters almost makes Smith lose hope.
In The Upright Citizens Brigade, they lampoon this trope. A guy says there's a truck full of letters supporting his cause, but they're just random letters like bills and coupons. And he just insists that there's a whole truck outside. And he's accused of having stolen a mailtruck to support his cause.
In It Could Happen To You, after a journalist (who masqueraded as a homeless man, to see how they would react: despite the fact they were penniless, they helped him out) runs the story about this poor couple, thousands of people send in contributions and raise $600,000 for the couple to live happily ever after.
In Sleepless in Seattle, after announcing how hard it is dealing with the death of his wife, the protagonist receives thousands of letters from around the country and one of them is the girl who he will eventually fall in love with.

Literature

In Harry Potter and the Goblet of Fire, people Rita Skeeter attacks in her Daily Prophet articles, such as Hagrid, Hermione and Harry himself, tend to receive large amounts of hate mail. Although it's not shown, Dumbledore claims that he was also sent a lot of letters vouching for Hagrid (from people who knew him from their school days). This is reversed in the fifth book when Skeeter is blackmailed into conducting an unbiased interview with Harry (also an aversion of this trope, since the resulting letters vary from "You're a hero!" to "Seek professional help".

Live-Action TV

On The Dick Van Dyke Show when Sally said on national TV that she was looking for a man Bags of Letters arrived overnight.
On The Late Show with David Letterman the Viewer Mail Theme Song (borrowed from The Perry Como Show) goes "Letters / We get letters / We get stacks and stacks of letters / LETTERS"
In the Hancock's Half Hour episode "The Bowmans" Hancock finds himself bombarded by mail the day after his radio Soap Opera character is killed off.

Music

In "Message in a Bottle" by The Police, the message gets 100 billion replies.

Theatre

In The Solid Gold Cadillac, Laura Partridge finally defeats the Corrupt Corporate Executives by adding up letters from small shareholders granting her voting control over their stock.
In Julius Caesar, Cassius forges letters, pretending to be Roman citizens, to persuade Brutus to take action against Caesar for the good of Rome. Achieves the same effect as honestly written letters.

Western Animation

On The Simpsons when they own a racehorse, as he's being put out to stud the horse gets Bags of Letters from prospective broodmares.
Also on The Simpsons, when Homer files a lawsuit against a seafood restaurant whose definition of "all you can eat" differed from his, the defendant asked for a display of how much Homer ate that night. At that point parodying the film Miracle on 34th Street, a huge convoy of people carrying large sacks enter the court, but it turns out that they just contain letters for an adjacent courtroom (People of Springfield vs Santa Claus, IIRC).

Real Life

Celebrities will frequently refer to "bags of letters" talking about fan mail or viewer feedback.
Robert Englund got so much fanmail when he played Willy on V that they eventually started to use unopened fan letters as props in other programs. In his biography, he mentions seeing a studio tour where the guide pointed to a stuffed letterbox and said, "All of those are letters to Willy."
The Canadian postal code H0H 0H0 was assigned for seasonal use in 1974, after letters addressed "ho ho ho" started arriving in Montreal (postal code H). A group of volunteers in that city's bureau de poste did not want the authors, mostly young children looking for Santa, to be disappointed.
Craig Shergold was diagnosed with a terminal illness. He made it known that he wished to break the world record for most postcards received before he died. He got better, and soon was up to his neck in cards.