Note: We don't have concrete examples for all of these, because they're based on a lifetime of watching millions of movies and countless hours of television. But please pipe up with your own favorites, and your own examples!
1. "Trust me, I'm a..."
The moment someone starts to pull rank or point out what an expert they are at something, they're quite possibly doomed. Nobody likes an expert, after all, and we all like to see experts fail, unless they're pilots and we're passengers on their airplanes. See also: "I know what I'm doing." Or: "I got this." Or: "Leave this to the professionals."
2. "You never said there would be..."
There's always one member of the team of good guys who's the squeamish one, and probably the comic relief. He's confronted with the one thing he fears or hates most — and usually overcomes his fear, before overcompensating and becoming toast.
3. "Stay here, you'll be safe."
Or, alternatively: "Go now!," which is frequently someone's last words before being sealed in a death trap. Or: "Get out while you still can." This sort of utterance can indicate a sacrificial lamb, or it can just mean that the speaker is going to "lead them off" or go do something dangerous, while the person being addressed is going to stay inside a confined, and supposedly safe, space. This always works out great, for everyone concerned.
4. "We're almost home free!"
Or alternatively: "It's not over!" The moment anybody either expresses confidence that the good guys have almost gotten away from the main danger, or insists that they're going to keep fighting no matter what, that person is quite probably marked for death.
5. "No matter what happens next, I want you to know..."
Or words to that effect — when someone is trying to get closure, or say that whatever happens today, they still feel some emotions, yadda yadda, this person is probably painting a giant target on his or her chest. Especially if this is said in the season finale (or worse yet series finale) of a TV show.
6. "I know I haven't been there for you in the past..."
Anybody who promises to be there for his or her loved ones from now on is not going to be there for his or her loved ones... it's like an unbreakable law of physics. The moment an absentee father, spouse, best friend or auto mechanic promises to be more reliable in future, you might as well stick a fork in him or her.
7. "I'm correcting a mistake I made long ago."
This one is almost cheating. When someone decides to redeem him- or herself for past mistakes, this usually means either outright self-sacrifice or some risky-ass behavior that adds up to the same thing. See also: "I have to do this." Or: "I've finally figured out what I'm supposed to do."
8. "Damn, I'm good."
Similar to item #1, when someone has just pulled off an amazing feat or shown incredible skill (akin, perhaps, to being a leaf on the wind), then that person is almost certainly about to be struck down. Especially if there's bragging or hubris or whatnot. See also: "Let's do this!" The one who's the most gung-ho is usually the first to die.
9. Any phrase containing the word "destiny" or "responsibility"
Someone who has a great destiny is probably safe from death — but the person who tells him or her about this epic destiny is probably marked for destruction. Any time you hear someone tell a hero that he or she is destined for greatness, the person saying those words is probably destined for immediate termination. (See, among others, Obi-Wan's last words to Luke Skywalker in the original Star Wars.)
10. "I'm all out of regrets."
Or similar wording, like "All of this was supposed to happen," or "I'm right where I'm supposed to be." Acceptance of fate = death. Even if the fate that someone's accepting has nothing to do with dying, and is just about accepting a situation. People who make peace with stuff might as well blow their brains out.
11. "You can do better than that!"
Or, alternatively: "Is that all you got?" Said tauntingly to an attacking evil person. Inevitably, that isn't all they've got.
12. "When all this is over..."
And finally, the classic. As often satirized on The Simpsons and other shows, the moment someone starts talking about all the great things he or she is going to do after this nightmare is finally ended, you know there's no happy ending in store for that person. In Hunt for Red October, as soon as Sam Neill starts talking about the great time he'll have living in Montana after he's defected, you know it's curtains for Sam — and we're not talking about picking out curtains for his Montana cabin.
Sources: We brainstormed most of these on our own — but to make sure we didn't miss any classics, we also glanced at TVTropes (here, here and here) and Wikiquote (here and here.) Thanks to Esther Inglis-Arkell, Kaila Hale-Stern and Katharine Trendacosta for the input!