I'm a big fan of the opening monologue in NieR: Automata.
"Everything that lives is designed to end. We are perpetually trapped in a never-ending spiral of life and death. Is this a curse? Or some kind of punishment? I often think about the god who blessed us with this cryptic puzzle...and wonder if we'll ever get the chance to kill him."
It's such a great hook, and it stuck with me throughout the whole game. What ends up making it so good isn't that its well-written or sets the tone or anything like the other examples posted here, but rather how this quote develops over the course of your playthroughs. Several games begin with a quote that gains meaning or clarity later on (starting with "is this a dream???" and later on learning that it is indeed a dream is a common cliche), but none stick out in my mind as going through several meanings and developments, each interpretation just as valid and impactful as the previous.