How we cite our quotes:
[Edward to Bella:] "[Carlisle] wasn't absolutely sure how his own transformation had occurred, so he was hesitant. And he was loath to steal anyone's life the way his had been stolen. It was in that frame of mind that he found me. There was no hope for me; I was left in a ward with the dying. He had nursed my parents, and knew I was alone." (16.64)
Edward talks of how Carlisle had prevented Edward's death by transforming him into a vampire. He may have ceased being human, but at least he got to live. However, Carlisle doesn't seem to think that life as a vampire is better than life as a human – he would only transform someone into a vampire as a last resort.
[Edward to Bella:] "The only way to be sure is to tear him to shreds, and then burn the pieces." (19.88)
As it turns out, even vampires aren't entirely immortal. Edward explains how to kill a vampire, which is what he plans for James.
Immortality must grant endless patience. Neither Jasper nor Alice seemed to feel the need to do anything at all. For a while, Alice sketched the vague outline of the dark room from her vision, as much as she could see in the light from the TV. But when she was done, she simply sat, looking at the blank walls with her timeless eyes. Jasper, too, seemed to have no urge to pace, or peek through the curtains, or run screaming out the door, the way I did. (20.178)
Bella is impatient as they wait for the tracker. She feels as if she is waiting for death. This passage also raises an interesting question: does time pass differently for vampires since they are immortal?