As much as I loved Infinite, there wasn't a single character in it remotely close to Andrew Ryan in terms of awesomeness. I find myself quoting him daily, but there's one line that I always remember, just for how chilling it was:
Before the final rat has eaten the last gram of you, Rapture will have returned. I will lead a parade. "Who was that," they'll say, as they point to the sad shape hanging on my wall, "who was that?"
Also, his monologue about burning down the forest on the surface was a great view into his perspective, and probably encapsulates his motives better than any other quote I can think of.
I did enjoy the banter of the Luteces in this game though, even if none of it was worth accurately remembering.
Me to this random girl : Mygirlfriendsayswhat? Random girl: What? Me: Zing!
Most of Bioshock has tons of rhetoric value. However, the most memorable for me was this one;
"I want a puppy, but that doesn't mean that I'm going to get one!"
This in reaction to the wish of Comstock to make Elizabeth his heir, even though he locked her up in a tower and isolated her from the world. Such a disjointed and innocent a comparison made me a father. Does she really want a puppy that much that she equates it to a lifestyle she describes as something indistinguishable from death?
Come all of Columbia! I will be your False Shepherd if it means my Elizabeth will get a puppy!