Rose spitting in Cal's face when he tries to force her into a lifeboat after she realizes he's framed Jack for theft and left him to die below deck. Cal's so caught off guard by this that Rose manages to slip free and run off to save Jack. The best part? Jack was the one who taught her to spit like that in the first place!
Also an excellent example of Throw It In; the original script had Rose stick him with a pin, until Cameron realized that making the spitting lesson into a Chekhov's Gun would work perfectly.
"I'd rather be his whore than your wife!"
The scene right before the ending, where Rose dies an old woman warm in her bed, and we see the photos on her mantel that tell us what she did after the sinking of the Titanic. Okay, so, she cut herself off from her family and had only her talents and determination to see her through after the sinking, and arrives in New York with absolutely nothing (except the Heart of the Ocean, but she never sold it or anything) and yet she still managed to fulfill her promise to Jack to live her life to the fullest, traveling and falling in love and raising children and everything. All during a time when it wasn't easy to be a woman, and it is never easy for someone so sheltered to strike out like that on her own. But she did it because Jack helped her realize that she had agency and free will in her own life (whereas Cal just wanted to control her), and she used that free will to steer her fate and fulfill her promise to Jack. Awesome. Rest in peace, Rose. You earned it.
The entire second half of the movie is one for the filmmakers. Specifically, the ship sinking in real time.
May also count as a Tearjerker, but the preacher towards the end, who continues preaching to his congregation even as the ship is going vertical, clutching at the hands of a few passengers as he holds onto a piece of the deck for dear life, and even so, he keeps talking. It somehow seems both sad and inspirational.
Unfortunately, some of the poignancy of the preacher's sermon is lost once the ship has gone under and he's so desperate to survive that when Rose comes to the surface and is trying to find Jack, the preacher is the one who pushes her under to keep himself afloat.
That was likely unintentional on his part. This troper is a lifeguard and trained to recognize when a person is actively drowning. When a person goes active, they start flailing about wildly to keep their head above the water, and it's not unheard of for them to grab or push someone under in this state.
The Unsinkable Molly Brown ordering the women in the boat to grab an oar, and the captain of the lifeboat refuses because they'd swamp the boat, and her reply, "I don't understand either one of you! What's the matter with you?! IT'S YOUR MEN OUT THERE!"
Sadly they missed (or dropped for the sake of time) an even better Real Life moment of awesome: The morning after, the Carpathia was spotted by the boat, and the guy at the tiller wasn't going to steer the boat over to it, saying it was to collect the bodies. What does Mrs. Brown do? Threaten to toss him overboard. The story may be apocryphal, but it would be in keeping with Molly's personality.
Another awesome thing omitted: by the time the survivors reached New York, Maggie Brown helped to form a committee to aid the financially poor survivers, was voted the head of it, and raised $10,000 for the cause. Keep in mind she did all this in a matter of days.
Adjusting for inflation, that's around $240,000.
Rose punching the guy that was trying to take her away from Jack, as well as how she searches for Jack instead of getting into a lifeboat in the rapidly flooding ship.
Rose telling her overbearing and selfish mother what we all were thinking "SHUT UP!"
Made even more awesome by the fact that it actually happened, as shown in the records of the inquest after the sinking. Lowe didn't know who Ismay was at the time, and saw only an arrogant and hysterical passenger.