What about this dude?
At the beginning of the film the camera pans from the street to a window - with closed curtains - and we hear a man (Kentley) screaming. Then we cut to an interior and Kentley is being strangled and on the very point of death. His scream stops, his eyes close and his head slumps.
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Then there is Yorick of ‘Alas poor Yorick’ fame.
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Unless it took you an hour and five minutes to compose this post, then, yeah, you didn’t read closely enough. 
Rebecca in the eponymous movie, IIRC.
You know, I thought of that but I only dimly know what that movie is about. From the plot summary on Wikipedia, it sounds like he qualifies.
True, but she (the Wicked Witch of the East) doesn’t enter into the story until after Dorothy’s house has killed her.
And, if ghosts count, Hamlet’s father. Though, even if ghosts count, he’s probably a bit too obvious for a trivia question.
Nope, the film opens with them alive and driving (and crashing, which is how they die). Oh, and that’s Constance Bennett, who appeared in the sequels when Cary Grant didn’t.
The OP can speak for himself, of course, but I like the idea of dead characters who are a lynchpin of the plot (like in The Big Chill) or dead characters who are a minor plot point or piece of trivia (as in The Good The Bad and The Ugly), more than ghost characters.
And I would argue for including the Wicked Witch of the East - you could argue that since the whole thing was something in Dorothy’s head while she was unconscious, she didn’t exist until Dorothy’s house fell on her. And even if she did have some objective existence at some point, since we never see her it doesn’t matter.
eta: ninja’d on my last point by Robot Arm.
Rather depends on the version. In the historical case, it’s usually accepted that the real Martin Guerre turned up during the trial. Different fictional adaptions then tend to handle that aspect differently.
For example, take the three best known recent versions. The 1982 French film follows the historical facts fairly closely and has someone claiming to be the real Martin appear at the trial. However - and it’s a while since I’ve seen it - while there’s some ambiguity about whether he’s not just another imposter, it’s clearly intended that he may well be the real one. By contrast, Sommersby handily meets the OP’s condition, since the notion is that having buried the real Sommersby at the beginning of the film, Richard Gere takes on his identity. Judging by the Wiki synopsis, in the stage musical it’s clearly the real Martin who comes back at the end.
My own suggestion: Falstaff dying off-stage in Henry V. No corpse as such, but the characters reminiscing about him makes for one of the play’s most famous scenes. Since he appears in the other plays, this is somewhat the equivalent of the Weekend at Bernie’s II example.
Which may be the first time anyone has compared Henry V to Weekend at Bernie’s II.
Henri Baq - killed at the beginning of the movie, his death was used to get Hemlock to agree to perform The Eiger Sanction
:: golf clap ::
Sifo-Dyas, the Jedi master who arranges for the creation of the huge clone Grand Army of the Republic in Star Wars: Attack of the Clones.
Charles Grady, Jack Torrance’s doomed predecessor as hotel caretaker in The Shining (and most of the people Jack later sees, for that matter).
Gazerbeam, who died on Nomanisan Island but left a crucial clue behind in The Incredibles.
The Detective. The victim is dead in the first scene.
Sylvia Lennox in The Long Goodbye.
Maybe Susie Salmon in The Lovely Bones, but I don’t remember if the first part of the movie is her alive or a flashback
Ah. So close… 
There was a movie in the '50s or early '60s I vaguely remember called “The Busy Body” which had much the same idea as “Weekend at Bernie’s”, except a couple of guys were moving the body all over New York trying to get rid of it. The featured actor in the film was Sid Caesar. I do not know who played the dead guy…It could have been Ben Blue, but I don’t know for sure.
Doesn’t he show up at the wedding? Not a flashback, even?
Sir Charles Baskerville’s (off-screen) death is what gets the plot moving in The Hound of the Baskervilles.
The father whose death kicks off the events of Death at a Funeral? I don’t remember off hand if he is seen alive or not.
In Treasure Island the treasure map (and the treasure) are from the long dead Captain Flint.
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Scraping the bottom of the barrel here but King Solomon was dead for centuries before the events in **King Solomon’s Mines.
**
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