I haven't done a study or anything, but the number of heroic deaths in popular entertainment seems to be on the decline. Not that I'm a great authority on the media; I haven't seen Titanic and I don't own a television. But it seems to me that very few characters these days get to make the kind of sacrifice that gets them into the annals of true heroes. I hate to see literary traditions that date back to Achilles on the downswing.
So what makes up one of these heroic deaths? A couple things are required. First, and most importantly, the death has to result in saving the lives of one or more people. There are a few loopholes here, as dying to preserve a culture or a way of life fits the bill, but let's not get too abstract. Peter Falk's character in The In-Laws actually dying to preserve the international monetary system doesn't cut it.
Secondly, the person has to know that taking the action that saves those lives will probably result in their death. If someone gets hit by a meteor while they pull a kid off a subway track, they may be a hero, but they didn't get a hero's death. On the other hand, staying in a burning building until it collapses in order to hand kids out to the firefighters is a world class hero's death.
The point of those two criteria is that a hero's death is ultimately a knowing sacrifice for the greater good, which are rare enough in life, and becoming rare in fiction. Dead heroes may be moving, but they make lousy sequel material.
Maybe knowingly sacrificing your life goes against the emphasis on safety that defines modern American culture. If the preservation of your life is drilled into you from birth, the idea of knowingly giving up that life looks more stupid than noble. If so, the loss to the American character is immeasurable. There are things worth laying down your life for. It's worth reminding us that this a virtue in entertainment. Maybe it will inspire a real person to pass kids out of that building, even when it isn't safe.