The death of 'Bull' McCaffrey from Backdraft, or at least his funeral in the end.
Rose dying (well, I think that she had) at the very end of Titanic (My Heart Will Go On has always had bad connotations for me, partly because of that, and partly because they played it during a high school awards ceremony at the point that I realised that I forgot to put my name down for!)
And while not actual deaths, there are two sequences that come to mind that are about conceptual deaths that make me weep.
The first is the ending of Nineteen Eighty-Four, where John Hurt's Winston Smith is staring at the image of Big Brother as the strains of Oceania 'Tis for Thee swell up. And he says three words that signal his complete death as a person. "I love you".
And the second, more recent one, is at the end of Rebuild of Evangelion 2.0: You Can (Not) Advance, when Shinji goes absolutely simian-fecal-matter trying to save Rei from the bowels (pretty much literally) of the Angel Zeruel. There's the touching and melancholy addition of a Japanese song called Give Me Wings, and then there's the fact that Shinji, without thinking (or more importantly, caring), is causing the end of the world by his actions.
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(No longer a mod)
On sabbatical...