Using quotes is a habit I picked up writing fanfiction for Criminal Minds, which is my favorite show, and starts and ends almost every episode with a quote. Usually the way I do it, is if I'm writing a short story, such as a fanfiction, then I start and end the entire story with a quote... if it's an original story that has multiple chapters, such as a novel or novella, I usually start each chapter with a quote, what do you guys think? Do you use quotes? Do you enjoy stories that use this kind of technique or would you rather the quotes were left out? (from a reader's perspective)
I've never read fanfiction, and I'm really struggling to understand what you're asking. Why would you enclose a whole story in quotes?
I think the OP meant something like... Chapter # “Something moving and thought-provoking.” - Some Famous Person ~*~ [Story text]
Tad Williams' Otherland begins each chapter with either a famous quote, a fictional news story clip or something else of relevant interest to the story. I liked that very much while reading it. It has to be done well but it definitely can be.
I have read quite a few books that use quotes either at the beginning of the book, or the beginning of each chapter. I like it.