Sequels are stories that take place after the original, often with most if not all of the same cast and frequently in the same setting if not the same location. If a work gets enough sequels, it becomes a Film Serial or Serial Novel. If they turn out to be bad, it's because of Sequelitis.
There are basically two kinds of sequels, planned and unplanned. An unplanned sequel is often the result of an author discovering, much to their delight, that the original did well and readers want more stories with their favorite dashing hero. In these cases the original is very likely a self contained stand alone story that does not require having read a Prequel to understand, often leaving no hints at what a sequel may have in store (or that there would even be one). This gives the author two choices for where to take the sequel: a simple rehash of the last adventure, with new locales and villains but with the same characters (plus a new Sidekick or Love Interest as an Audience Surrogate for those who didn't see the original), or try to go for a more epic arcing story. This is done by exploring the existing mythology and Backstory that the original establishes (or weaving one in wholecloth if the original didn't have one). As you can tell, these are foolproof choices.
If it's a planned sequel then the savvy author will have at least a rough draft or idea of what happens in the sequel(s), what happened in the prequel, and leave in various Sequel Hooks and Schrodingers Guns in the original to later link it with any following stories. These plot hooks will likely be vague enough that the sequel(s) aren't constrained to go in one specific direction. If you ever run into a film that has an unusual, niggling plot detail that is never solved, it may well be because the author hoped for a sequel that never happened. And that makes us sad.
The relationship between a sequel and Prequel is a close one. Like the sequel, the prequel is by definition made after the original has been released, but takes an earlier place chronologically inside the same story while the sequel takes place after. Essentially, all prequels are sequels of a sort.
For much the same reason Hollywood likes to make adaptations of existing works from other media or Remakes of older films, big film studios would love for every film they have to become a series and earn lots of cash. There are a lot of marketing advantages to this: a pre-existing fan base, is easier to write (especially if the film series is going on a novel-per-film rate) and the actors likely had a popularity boost from the original, bringing more viewers in.
Of course, the idea of a sequel is Older Than They Think. William Shakespeare himself wrote The Merry Wives of Windsor as a follow up to a group of historical plays (Henry IV, Henry VI Part 1, Henry VI Part 1, Richard II, and Richard III, while Antony and Cleopatra could be considered one for Julius Caesar. Centuries before even that, Homer wrote The Odyssey as a sequel to The Iliad
No examples please, we'd be here all day.
- Artifact Title: When a title relates to the first story, but not to the sequels.
- Capcom Sequel Stagnation: When a game gets released many times with small changes between versions.
- Contested Sequel: When some of the audience likes the sequel and others don't.
- Dolled-Up Installment: Practice of inserting a work into a franchise which it was not originally intended for.
- Even Better Sequel: When an installment is good but the next one is better.
- Fan Sequel: When fans decide to make a sequel.
- First Installment Wins: A piece of media receives one or many sequels, but the original is the one everybody loves and remembers.
- Franchise Zombie: Franchise lasts longer the author intended for.
- Happy Ending Override: Sequel starts out with a previous victory negated and things much worse than when they began.
- Immediate Sequel
- Interquel: A sequel set in between a period of time established in a previous work.
- Legendary in the Sequel: When the main character from a prior work is made into a legend.
- Mission Pack Sequel: Same game, different levels.
- Non-Linear Sequel
- Numbered Sequels: When a sequel title has a number.
- Sequel Number Snarl: When the numbering of sequels gets... odd.
- Oddly-Named Sequel 2: Electric Boogaloo: Weird sequel subtitle.
- Pandering to the Base: Doing what fans want instead of what the creators and executives want.
- POV Sequel
- Prequel: Sequel set before the original.
- Prequel in the Lost Age: Sequel set in the time the original says has long passed.
- Refitted for Sequel
- Ridiculous Future Sequelisation
- Running the Asylum: Hired fans turn fanon into canon.
- Saved for the Sequel
- Sequel Displacement: When previous installment of a series is less known than the most popular one.
- Sequel Difficulty Drop: Sequel is easier than its predecessor.
- Sequel Difficulty Spike: Sequel is harder than its predecessor.
- Sequel Episode: The plot or resolution of a Stand Alone Episode in a series gets revisited in a later episode.
- Sequel Escalation: Attempts to make a sequel to have elements of the previous installment, but more of them.
- Sequel First: A sequel is released in a foreign market before the first installment.
- Sequel Gap: A fairly long time passes between an installment and its sequel.
- Sequel Goes Foreign
- Sequel Hook
- Sequel Non Entity: Hey, they reduced the Five-Man Band to a Power Trio! What happened to the other two characters?
- Sequel Reset
- Sequelitis: As the number of franchise installments goes up, the quality of them goes down.
- Sequelphobic: When a announced sequel is not welcome, despite its actual quality.
- Sequel Series
- Stealth Sequel
- Stopped Numbering Sequels: First, sequels of the series had numbers, but then not.
- Sudden Sequel Death Syndrome
- Surprisingly Improved Sequel: Sequel is better even though predecessor wasn't that good.
- Thematic Series: Movie sequels that don't necessarily follow the same continuity or characters.
- Third Is 3D
- Un Installment: A work that doesn't actually exist nevertheless has a sequel.
- Word Sequel: The sequels follow this pattern: Name, Name II, Name III, Name: Word.
- Your Princess Is in Another Castle: It looks like the story or arc has ended, then another world/villain/problem appears.