Related is a style that was popular in the 19th century where the narrator is telling a story they were a part of after the fact as if writing a letter to you about the events. Typically, while they were a witness to the events, they were not an active participant, though this was not always the case. Frankenstein was told by the titular doctor to a third party (the reader) after the events resulting in his re-animation of a corpse and the resulting monster. "The Strange Case of Dr. Jekyll and Mr. Hide" is told from the point of view of a lawyer friend of the doctor after the events of the story. Edgar Allen Poe often used this in his short stories, with the added twist that the narrator is the villain of the work (The Telltale Heart is the murder describing the descent into madness he felt after killing a man on a whim. The Cask of Amontillado is told as a confession by the narrator after he buried a man alive as a revenge for an unknown slight that the victim committed against the narrator.
The Japanese film Rashomon is told from the point of view of a pair of witnesses to a court proceeding in which three conflicting stories are given by the three people as to which one of them murdered the Samurai. (Our focal point characters witnessed the lead up and the aftermath of the murder, but not the circumstances as to who killed the Samurai. Thus our POV characters are able to verify that the three witnesses were all at the crime scene at the same time... but not whodunnit). The three participants all tell contradictory stories, all of which turn out to be confessions that the participant is the sole party responsible for the murder (which many parody or homage series fail to get correct. In those, the characters tell contradictory interpretations of what happened to implicate another character and exonerate themselves.)
Sherlock Holmes is told from the point of view of Watson, the detective's partner who is amazed at Holmes' skills (modern adaptations tend to actually play up Watson's role in the story... it's not that he is incompetent... he actually is... Holmes is just better.). The use in the series has led literary critics to develop the terms Doylist and Watsonian (the terms refer to using explanations for plot choices and whether the critique uses information that the creator used as part of his/her creative process vs. information that is internal to the story only).
Edit: Additional Answers
Related is a style that was popular in the 19th century where the narrator is telling a story they were a part of after the fact as if writing a letter to you about the events. Typically, while they were a witness to the events, they were not an active participant, though this was not always the case. Frankenstein was told by the titular doctor to a third party (the reader) after the events resulting in his re-animation of a corpse and the resulting monster. "The Strange Case of Dr. Jekyll and Mr. Hide" is told from the point of view of a lawyer friend of the doctor after the events of the story. Edgar Allen Poe often used this in his short stories, with the added twist that the narrator is the villain of the work (The Telltale Heart is the murder describing the descent into madness he felt after killing a man on a whim. The Cask of Amontillado is told as a confession by the narrator after he buried a man alive as a revenge for an unknown slight that the victim committed against the narrator.
The Japanese film is told from the point of view of a pair of witnesses to a court proceeding in which three conflicting stories are given by the three people as to which one of them murdered the Samurai. (our focal point characters witnessed the lead up and the aftermath of the murder, but not the circumstances as to who killed the Samurai. Thus our pov characters are able to verify that the three witnesses were all at the crime scene at the same time... but not who dun it). The three participants all tell contradictory stories, all of which turn out to be confessions that the participant is the sole party responsible for the murder (which many parody or homage series fail to get correct. In those, the characters tell contradictory interpretations of what happened to implicate another character and exonerate themselves.
Sherlock Holmes is told from the point of view of Watson, the detective's partner who is amazed at Holmes skills (Modern adaptations tend to actually play up Watson's role in the story... it's not that he is incompetent... he actually is... Holmes is just better.). The use in the series has often lead to literary critics to develop the terms Doylist and Watsonian (The terms refers to using explaination for plot choices and whether the critique uses information that the creator used as part of his/her creative process vs. information that is internal to the story only.).
Edit: This title comes up a lot in Television shows and films. For example, for example, in the Muppet's Christmas Carol, Gonzo is cast as "Charles Dickens" who never was a character in the source material. Most of Gonzo's dialog is lifted straight from the narration of the book, resulting on what many fans of Dickens believe is the best film adaptation of the book (since the book has some amazing narration that previous adaptations ignored.). In the Doctor Who Christmas special, "The End of Time," the first half of the special includes a narrator (to make the episodes feel more like a classic Christmas special) telling the story of the Doctor's adventure... the first part ends on a cliffhanger that the narrator is not just a character who exists in this story, but is the true bad guy of the story and has been behind all the other characters actions.
Other shows, especially comedy, use a narrator as a character that the heroes and villains can interact with. For example, the English dub of Samurai Pizza Cats has a narrator who the trio of titular heroes (and anyone else for that matter) engage with, often getting into frequent verbal arguments with over the direction. In the Disney Channel Cartoon "Dave the Barbarian" the on screen characters are able to interact with the narrator, who occasionally will also get upset that the heroes present happenings fail to live up to the dramatic narration the narrator chose to open the episode with. In the series finale, the heros' greatest foe, the Dark Lord Chuckles the Silly Piggy (in case you didn't realize this was a comedy spoof) realizes that all his plots weren't foiled by Dave and his family, but rather the narrator always narrating that Dave and his family foil Chuckle's plans... so he kidnaps and hypnotizes the Narrator and has him narrate the story where Chuckle's always wins. This works until the narrator loses his voice (causing the plot to literally stop) and the show has to get the Narrator's understudy to come in... who isn't hypnotized, but hasn't a clue what the show is about beyond the title... so Dave and his family win, but all the characters are turned from characters from a medievel fantasy setting to a space opera setting confusing everyone in the process.
In the Animated Film Hercules, we get a narrator (named Bob in the Animated Series) voiced by Charlse Heston giving a dramatic read... until the Muses tell him that this is too much melodrama for the audience and with "Bob's" Permission they take over the narrative of the story, setting up the narration with energetic Gospel Music rather than a solemn academic reading of lines (It's also a pun... the Muses are a Greek Chorus... a type of narrator common in Greek Plays... because they are all Greek Goddesses of the Arts and "Proclaimers of Heroes" like Hercules. Because of this, they are actually in the story proper and interact with characters, albeit only during the song sequences (Most prominently in Meg's song "I won't say I'm in Love" where they provide the backup vocals and try to push Meg to accept that it's okay to love someone again.), however, they have no direct impact on the plot.