How we cite our quotes: All quotations are from Titanic.
Quote #1
JACK: You don't want to do this.
Jack and Rose meet when Rose is contemplating throwing herself off the back of the Titanic. Jack's not convinced that Rose genuinely wants to die, and manages to get her to calm down/try to get back over the rail.
Quote #2
JACK: Listen to me, I've got you. I won't let go. Now pull yourself up, come on!
"Not letting go" is a big theme in the movie—you'll see that phrase come up again and again. In this first instance, Jack is trying to get Rose back over the railing…but she slips. Luckily for Rose, Jack remains very committed to keeping Rose alive throughout the movie.
Quote #3
JACK: No, no, that's not what I was thinking. What I was thinking was, "What could have happened to this girl to make her think she had no way out?"
When Jack and Rose talk later, Rose is worried that Jack thinks badly of her, given that she's clearly so privileged and, yet, was trying to kill herself. Jack explains he's not the judgmental type—really, he was just interested in knowing why she was so distraught.
Quote #4
JACK: I don't think so. They've got you trapped, Rose, and you're going to die if you don't break free. Maybe not right away because you're strong, but sooner or later, that fire that I love about you, Rose…that fire's going to burn out.
ROSE: It's not up to you to save me, Jack.
JACK: You're right. Only you can do that.
Having explained earlier that she's basically miserable and trapped in her relationship with Cal, Rose is now trying to convince Jack that it's all good—and that he needs to leave her alone. He isn't having any of it, since he thinks that Rose's current life will eventually kill her, one way or another.
Quote #5
JACK: Don't you do that. Don't you say your goodbyes. Not yet.
At the end of the film, Jack and Rose are literally chilling in the water, the boat having sunk, and Rose tells Jack that she loves him. That's a nice sentiment, but it makes Jack nervous, since he takes it as Rose saying her goodbyes.
Quote #6
JACK: You must do me this honor. You must promise me that you'll survive. That you won't give up, no matter what happens, no matter how hopeless. Promise me now, Rose, and never let go of that promise.
Before Rose can get too down in the dumps (she's freezing in the Atlantic, after all) Jack makes her promise that she's going to keep fighting her way through their current predicament—and any others that might arise.