On screen deaths: It's gotta be Hard Boiled! I mean sweet jesus! the last 20 minutes of that film was just dozens of people being blown away! I recon at least 250 deaths were shown in that film!
As for implied deaths...well that a bit of a pointless question. Everybody on earth dies in Strangelove...Star Wars sees the death of some other planet. Body count means bodies damnit!
EDIT: Not too far off!
From IMDB:
http://www.imdb.com/title/tt0104684/trivia
"Hard Boiled - Body Count: 230."
"Has more on screen deaths than any other film."
In the words of Duke Nukem: Damn! I'm Good!