Two-Act Structure

The story is neatly divided into two parts. The first part will be lighthearted and straightforward compared to the second, which will wrap things up in a realistic mixed-bag sort of way. This structure is most common in musicals. It comes in two flavors: the rise-and-fall variety, which has everything on the up-and-up in the first act and, in the second act, shoots it all to hell; and the parallel variety, where the darker, more intricate and realistic second act makes some sort of point about the first act.

Often, the dark turn will be heralded by the last moments of the first act. A sizable period of time between the two acts is also commonplace.

There must be a change in tone for this trope to apply. Andrew Lloyd Webber's Phantom of the Opera, for instance, divides its two acts at a good stopping place in a continuous progression, nothing more, and so this trope doesn't apply to it.

Examples of Two-Act Structure include:

Rise and Fall

Film

Titanic (VHS edition): the first cassette ends with the crash and Mr. Andrews' pronouncement of doom.
The Sound of Music, with the second 'act' beginning after the marriage and the Nazi takeover.
- Done more subtly in the stage version, where "Climb Every Mountain" is the Finale Act One and the marriage and Anschluss take place in the middle of the second act. So the turning point turns out to be less to do with dramatic events than with Maria's realisation of herself as a character.
Scarface: Act One is about Tony Montana's rise to the top of the Miami underworld, while Act Two is how everything goes straight to hell.

Literature

This accurately describes the entire Harry Potter series, with the turning point being Harry Potter and the Goblet of Fire, where Voldemort is reborn and suddenly Anyone Can Die. Fittingly, A Very Potter Musical has the act break right in that very spot, and while it remains a light-hearted parody, the characters still feel like they're going through hell.

Live-Action TV

The television show Skins keeps the same cast for two seasons before starting over with a completely new cast and story; each "generation," as they are called, tends to roughly follow the Rise and Fall pattern, with a somewhat simpler, sunnier first season followed by a Darker and Edgier second season where things start falling apart.
Stargate shows split their seasons into two parts, often having some kind of cliffhanger or game-changer before the intermission.
Many a U.S. Sitcom up until the 1990s used a two act structure, with a plot twist at the commercial break and a second act where the Zany Scheme fell apart, restoring the status quo.

Theatre

The Rise and Fall of the City of Mahagonny
Camelot; for that matter, the Arthurian mythos and all works based on its whole.
Fiddler on the Roof, with the Cossacks' invasion of the wedding as the turning point.
Wicked
Avenue Q: Both halves are funny, but by the end of Act 1 most of the characters have fundamentally screwed up somehow; Act 2 focuses on them realising what they've done wrong and making amends.
Paint Your Wagon
Shakespeare's tragedies tend to go this route, particularly Romeo and Juliet. The first part, taking up Acts 1 and 2 and the first half of Act 3, is your basic tragicomic affair, but the second part, after Tybalt kills Mercutio and Romeo kills Tybalt in vengeance, is where it all really goes to hell.
- Bernstein was aware of this. In West Side Story, he puts the Rumble (where the deaths of Riff and Bernardo parallel those of Mercutio and Tybalt) just before the interval.
Ragtime: Where Act 1 is an endearing tribute to the pratfalls and triumphs of the oughts (with an against-all-odds love story to boot), Act 2 begins with the prescient child-narrator dreaming about (soon to occur) explosions and with Coalhouse firing a rifle indiscriminately from a clocktower.
Jeff Wayne's The War of the Worlds; Act I describes the conquest of Earth by the Martians, and Act II its aftermath.
Jesus Christ Superstar: the break comes between Jesus's lament for Jerusalem and Pilate's first appearance. It's all dark, but the second act is darker than the first.
In Little Shop of Horrors, the first act ends after Orin's death-the first point at which Seymour really kills.
Merrily We Roll Along purposely inverts this trope; since the plot runs backwards, Act I is where Frank's life has already gone to hell, whilst Act II is sees him becoming younger and thus more promising and optimistic.
Into the Woods wraps up its massive fairy-tale crossover as neat and tidy as a military-school bunkroom in the first act, and then goes into the repercussions of everyone's means of getting their happy endings with a far-less-defined sense of what to do, brought home by killing the Narrator.

Parallel

Anime and Manga

Much like Into the Woods, the anime Princess Tutu, the first season has dark moments, but is overall a happy Magical Girl romp through fairy tale tropes with a ballet twist. The season even ends in a way that makes it seem like the ending of a typical fairytale, with Mytho and Princess Tutu dancing happily together after their victory against Princess Kraehe. The second season, however, seems more like a deconstruction of a fairytale, with Mytho being poisoned by Raven's blood and becoming a villain, character's motivations being questioned and dark backstories revealed. Edel's Catch Phrase--"May those who follow their fate find happiness, may those who defy it be granted glory"—takes on a whole new meaning when looking at the two seasons of the show.

Film

The Princess Bride, with the turning point being Westley's capture.
Life Is Beautiful. First half, light-hearted romantic-comedy. Second half, heartbreaking tragi-comedy set in a concentration camp.
Akira Kurosawa was quite fond of this trope:
- Ikiru. The first act takes place after the protagonist, Watanabe, has been diagnosed with terminal cancel and in the second half we learn of the good Watanabe did after during his final months during his wake.
- High and Low- First act is about ransoming with a kidnapper. The second act is about finding the kidnapper and bringing him to justice.

Theater

The Fantasticks has its two acts explore the difference between forbidden love and real love.
Rent, complete with a shift in storytelling pace (the first act takes place in a single night, and the second act takes an entire year).
A Madhouse in Goa by Martin Sherman.
Dreamgirls. The first act is about the girls' rise to stardom and subsequent challenges, and ends with Effie being kicked out of the group as her replacement is brought in. The second act opens 8 years later. Deena and Curtis are married, and Effie is a single mom on welfare with Curtis' child, and decides to give a shot at a solo career.
Waiting for Godot subverts this by having the second act be more or less the same as the first, without much difference in tone. Hence the reviewer who said that it is "a play in which nothing happens, twice."
Spring Awakening is a curious case since although most of the tragedy happens in Act II, the real shift in storytelling is actually in the middle of Act I, right around where Moritz flunks and Melchior and Wendla's romance takes a serious turn. However the two acts do complement each other nicely as Act I is about sex (i.e. life) and Act II is about death.
Sunday in The Park With George. Act I ends with the completion of Georges Seurat's most famous painting; Act II picks up after a Time Skip of nearly a century and explores the 20th century artistic struggles of Georges's Identical Grandson.
Heathen Valley has a very optimistic ending to act one, where everything seems to be going right. Then act two starts up with tenser undercurrents, leading to the end.