[Henry:] I hate to be where [Clare] is not, when [Clare] is not. And yet, I am always going, and she cannot follow. (Prologue.15)
Henry comments on the fact that not even his love for Clare can overcome his displacement in time and space. His genetic disorder is stronger than his emotions, stronger than his will.
[Clare to Henry:] "…it's very peaceful here with you. It's nice to lie here and know that the future is sort of taken care of." (1.1.15)
Clare believes in that moment of finally finding Henry in the present. She considers her future to be taken care of, and this means there's nothing to worry about anymore but to enjoy being with Henry in the moment.
[Henry:] "A couple years ago, I saw a little girl get hit in the head with a hockey puck at Indian Head Park. […] I found out later that she died in the hospital. And then I started to time travel back to that day, over and over, and I wanted to warn her mother, and I couldn't. […] It was like being a ghost." (1.4.59)
Henry tried to save the girl several times, and every time had to witness her death happen once again, helpless. It makes you wonder if it's easier to accept death when you know there's nothing you can do or could have done. That it's just a fact of life.
[Henry to Henry:] "I was just talking about that with a self from 1992. […] he thinks that there is only free will when you are in time, in the present. He says in the past we can only do what we did, and we can only be there if we were there." (1.4.64)
Older Henry explains to younger Henry that because you have already lived your past, you can't change what happened, which means you have no free will even when popping back to those times. But you can choose how you want to live your life in your present.
[Henry to Henry:] "But […] you have to behave as though you have free will, as though you are responsible for what you do. […] Apparently, if you don't, things are bad. Depressing." (1.4.64)
Henry suggests that if you don't take responsibility for your actions, you'll feel no control over your life and therefore your life won't mean anything to you. He believes that a sense of purpose in life is the key to happiness.
[Henry to Clare:] "[…] I had this huge crush on Parry Hearst […] She was a rich California girl who got kidnapped by these awful left-wing political terrorists, and they made her rob banks. […] I guess I kind of knew how she felt, being taken away and forced to do stuff she didn't want to do, and then it seemed like she was kind of enjoying it." (1.4.132-136)
Henry admits to his ambivalent feelings about his time-traveling condition. On the one hand, he feels trapped and like a victim, on the other he enjoys not having a choice but to go on the ride.
[Clare to Henry:] "I thought free will had to do with sin." (1.4.241)
Because Clare has been raised Catholic, the idea of acting out of your own will, and not the will of God, appears to be a sin to her.
[Henry to Clare:] "[…] if you are feeling boxed in by the idea that your future is unalterable, imagine how I feel. I'm constantly running up against the fact that I can't change anything even though I am right there, watching it." (1.4.246)
Henry explains to Clare that while she feels like she has no choice in what her future will bring, Henry has seen and experienced his future, which makes it that much harder for him to act as if he has complete free will.
[Clare to Gomez:] "I love him. He's my life. […] With Henry I can see everything laid out, like a map, past and future, everything at once, like an angel. […] we're part of each other." (1.8.201)
Clare explains to Gomez that since she has grown up with Henry, he's become her life – all of it – past, present, and future. In some way, they have lived all of it already.
[Clare:] I never chose Henry and he never chose me. So how could it me a mistake? (1.8.217)
Clare believes that because their match was made by time, or the laws of the universe, and not by them, the choice shouldn't be subject to human error – it has to be the right choice. Does she have a good point here?