Huh? Have I been whooshed?
How about Fallen, in which we find out that Denzel Washington’s character is dead and a demon is inhabiting his body?
And every vampire movie, of course.
How about not? Washington isn’t possessed until the end of the movie.
No, gobear’s right–Denzel’s character is dead at the moment of the movie start. The whole movie’s a flashback after the opening narration: “This is about the time I almost died…” With the end being the twist about whose narration it really is, of course.
Does it count if only his career is dead?
Beetlejuice?

Point Blank (1967)and High Plains Drifter both feature main characters who are essentially ghosts come back to avenge their own murders.
I suppose Rashomon might count since one of the main characters is the murdered husband, who tells his tale from the dead. When the film starts the two travellers are discussing the central ambush/rape/murder that has already happened before the movie starts.
In the 1946 and 1964 versions of The Killers, the central character is murdered in the opening moments. Each man’s story is then played out in flashbacks.
I’ll take your word for it. I haven’t seen the movie since it was in the cinemas, so it’s more than likely I forgot a minor detail somewhere.
Does it count if he doesn’t realize he’s dead? The Sixth Sense
GoBear is 100% on this one. It was the big twist of the whole flick.
T-i-i-i-ime is on my side!
A Perfect World.
The movie opens with a shot of Kevin Costner lying peacefully in a grassy field. Then they flash back to show you how he got there. The movie closes with a shot of Kevin Costner lying peacefully in a grassy field…but shown from a different angle, so you can now see the bleeding bullet hole in his chest.
Lawrence of Arabia begins with Lawrence’s death on a motorcycle (you see him mount the cycle but never hear him speak) then the narrative begins as admirers and detractors discuss him at his funeral.
As memory serves, I, Claudius begins with Agrippina and Nero looking at the dead body of Claudius, whom they have murdered, then finding his autobiography, which tells the story from a generation before his birth to his death. (At the end Claudius’s spirit has a discussion with the Sibyl in which the future for most of the characters and the Empire is discussed.)
The Others
Titanic
Ghost
That’s an obvious one, but it works.
But he wasn’t dead at the beginning of the film. He died at the end of the first scene. Depending on how far into the movie we can do this, there’s also What Dreams May Come and All Dogs Go to Heaven. 
Grave of the Fireflies. Like American Beauty and Sunset Boulevard the dead character is actually narrating the opening lines.
I don’t know why we have to exclude these movies based on this. Not all biographical movies adopt this format. For example, in Chaplin, starring Robert Downey, Jr, the main character is old but not dead.
In that spirit, i offer Immortal Beloved, starring Gary Oldman as Ludwig von Beethoven.
Also:
Ken Loach’s Land and Freedom, starring Ian Hart.
Thanks for sharing 
One of my favorite movies of all time, actually:
Shallow Grave
Um, did i miss something the three times i saw that movie?
Which main character is dead at the start of the film?