Present Absence

A character who does not actually appear for much, if not all, of the plot, but whose presence is nevertheless felt immensely. More accurately, the fact that this character is gone has as much if not even more of an effect on the plot, the characters, and the audience than any appearance they might have had.

Rather than show their importance by giving them dramatic scenes or crowning moments, these works give us their character by constantly showing what effects their absence has on the world and the characters, be it through constant reflection,a character following their requests, or dedicating himself to following their example. Alternatively, the character, in his absence, still pulls strings or drives characters' actions, becoming a sort of MacGuffin or shadowy influence.

In short, the character drives the plot despite never having to be shown, be it directly or through the minds and hearts of the characters. This can usually done in a few ways:
 * The character is absent for the main part of the film, but subtly guiding the characters' actions, and then reappears later.
 * The character appears in the first part in the movie, and then dies or disappears, leaving the characters to carry on their memory.
 * The character's actions or ideals, or even the mere event surrounding their death or disappearance, have repercussions and effects that last long after their death, be it positive or negative, tangible effects or inspiration.

Compare The Unseen. A Posthumous Character is influential despite being dead and a Dead Little Sister because of it. A Super-Trope in many ways to Parental Abandonment.

Anime and Manga

 * Nagi Springfield in Mahou Sensei Negima. He's only seen in flashbacks, but is Negi's primary motivation for doing just about everything.
 * in Tengen Toppa Gurren Lagann. Gets killed off only eight episodes in, but everything else accomplished in the rest of the series is largely accomplished thanks to the fighting spirit he inspired in the rest of the main characters. He (or at least the character's memory of him) even pops up during the final battle to bring everyone to their senses after getting trapped in a Lotus Eater Machine.
 * in Legend of Galactic Heroes. After his death, his absence has as much of an influence on the characters, particularly, as his presence did.

Comic Books

 * Thomas and Martha Wayne in any Batman media.
 * Likewise, Uncle Ben in Spider-Man.
 * The Comedian in Watchmen.

Film (Animated)

 * Ellie in Up, in a very major way. While she doesn't appear in person after the first five minutes, her presence is felt in every scene.

Film (Live Action)

 * "Where's Doug?" — The Hangover.
 * in Noroi the Curse.

Literature

 * Dr. Murry in the novel A Wrinkle in Time.
 * Sirius Black in Harry Potter does this a few ways:
 * In Prisoner of Azkaban, he plays the "shadowy but unseen figure that drives the adventure", and between Azkaban and Order of the Phoenix, he serves as a symbol of a happy future and the family Harry could have.
 * Since Order of the Phoenix, his death weighs down Harry terribly, especially in The Half Blood Prince.
 * Dumbledore plays this a lot more straight in Deathly Hallows, where not only does he have a posthumous plan that weaves all the characters through it, but his death throughout the novel symbolizes the hopelessness of Voldemort's rise to power: no one is safe, evil is everywhere, and there's no beacon of hope to which to turn. While others turn to Harry, Harry himself, being used to turning to Dumbledore, is lost, and then becomes incensed when his perfect image of Dumbledore is challenged.
 * Also, Harry's parents for the whole series, even though they died before the first chapter of the first book.
 * Rand al'Thor (the Dragon Reborn) was almost entirely missing from The Dragon Reborn. He still had enough effect on the plot to name the book after him.
 * Sauron in The Lord of the Rings. The eponymous Evil Overlord does not appear in person once in the entire work, and his only lines are delivered after the fact by the character to whom they were spoken (Pippin, describing what he saw in the palantír).
 * The title character of Daphne Du Maurier's novel Rebecca. She's dead, yet influences everything and everyone around her.

Live-Action TV

 * The live-action Birds of Prey show has this. The absence of Batman and Catwoman deeply affected the Huntress (their daughter and central character) and the absence of The Joker motivated Harley Quinn [the Big Bad].
 * John Winchester in Supernatural
 * Later on God becomes this as the brothers are trying to figure where He went and why He is not acting to stop the coming Armageddon. The demons and the top angels decide that they have free reign to 'finish things' while Castiel is struggling to figure out what God wants him to do.
 * In the first season of Heroes, Sylar gets relatively little screen time, but his presence is felt everywhere. This is especially true for Matt Parkman's storyline, in which he is hunting Sylar.
 * in Blake's 7.

Theatre

 * The deadbeat dad from The Glass Menagerie, a Tennessee Williams play. He never shows up in person, and is mostly mentioned in the introduction, but his absence is pretty significant.
 * Godot (the one for whom they're waiting)
 * General Gabler in Hedda Gabler.

Video Games

 * Darth Revan in Knights of the Old Republic 2.
 * Alex Mercer in Prototype. He pretty much single-handedly kick-starts the entire conflict of the game.

Web Comics

 * Girl Genius has the Heterodyne Brothers, particularly Uncle Barry.
 * Lord English from Homestuck. Despite him the only view of the Lord himself being his absurdly long coat. And yet during the fourth and fifth Acts, his presence pervades the narrative and gives it an intensely desolate feel.