Ralph Bakshi's Wizards was a fantasy film set after an apocalypse.
Battle for Terra takes place after Earth, Venus, and Mars have wiped each other out, and the survivors are traveling on a Generation Ship that's breaking down, looking for a new planet to settle. They find a habitable world and call it Terra. Of course, there are two problems: the air is poisonous to humans, and there are natives to consider. Another example is the Terrans themselves, who used to have advanced technology but nuked themselves back to the Stone Age.
In Final Fantasy: The Spirits Within, humanity is forced to live in shelters that protect them from the Phantoms, creatures that kill living beings by stealing their souls by touching them.
Films — Live-Action
The Book of Eli has Denzel Washington in a world decimated for an unknown reason (heavily implied to be nuclear warfare) and literature, most notably the Bible was blamed.
Stalker takes place in a devastated area called The Zone.
In Buck Rogers in the 25th Century, much of the Earth has been reduced to a desolate wasteland by a nuclear holocaust, inhabited by mutants. The surviving humans (or rather, their descendants) live in isolated, hi-tech cities. In the TV series that followed, however, the Earth was depicted as being much more hospitable.
The Matrix is set in the aftermath of a Robot War that the humans lost. The free remnants of humanity are holed up in the last human city, Zion, while everyone else is grown and plugged into a machine-made world called the Matrix. The films are about the human resistance against the machines, and the effort to free the rest of humanity from the Matrix.
Logan's Run is set on a post-apocalyptic Earth where the only survivors live in a hermetically-sealed domed city — except for one crazy old man who lives in the U.S. Capitol with his cats.
Taken to an extreme in The Time Machine where Alexander travels to the year 802701, where humanity has started over and split into the normal-looking Eloi and the savage Morloks, and then again to the year 635,427,810, where the latter has taken over the planet.
Waterworld takes place after the polar ice caps have completely melted due to a magnetic pole reversal, causing the all remaining human civilization to become seafaring.
The Postman is a post-apocalyptic world where civilization starts to rekindle after the hero delivers their old mail.
The Big Reveal at the end of MST3K classic Teenage Caveman.
Warrior of the Lost World, an Italian rip-off of Mad Max with none of that franchise's charm. Or much of an apocalypse for that matter, given how lush and green the 'lost world' is. To look at it, you'd think that all the likable people in the world simply went on vacation and told the cast of characters that we see that they'd all died.
Exam has a minor example, as the story takes place in the aftermath of a global pandemic.
Total Recall (2012): After a series of wars over resources, the only parts of the world left that aren't biohazard wastelands are the United Federation of Britain (a chunk of Europe controlled by Britain) and the Colony (Australia).
The docu-drama The Age of Stupid portrays Earth in the year 2055 after runaway climate change ravages the planet. The film is shown from the viewpoint of an unnamed Archivist - the last surviving human on Earth - who laments "why didn't we save ourselves when we had the chance?", and plays back real documentary footage from 2008, when the film was made.
After Earth: Humans have left the earth for an as of yet unknown reason.
Reign of Fire: Human civilisation is destroyed when they inadvertently awaken the dragons who had been buried. It's implied that they had previously wiped out the dinosaurs too.
Stake Land: Unique to the genre, its after a Vampire epidemic wiped out most of the human race (which had a lot of help from a Naziesque Cult called the Brotherhood).
Cloud Atlas—The last portion of the film, at least chronologically, is entitled "Sloosha's Crossin' an' Ev'rythin' After." This section takes place in Hawaii years after an unspecified apocalyptic event, and the remnants of human kind has been divided between peaceful valley men (including Tom Hanks' character Zachary) and murderous cannibals called Konas (including the chief, played by Hugh Grant).
The story of Snowpiercer picks up 17 years after mankind's attempt to fight global warming through geoengineering failed and the chemical compound they emitted into the atmosphere turned Earth into an ice globe.