I stated in an Anacrusis LJ feed comment-thread, last week, that Memento had more structural influence on my writing than basically anything ever. I realized later that that’s not exactly true; it did have a lot of influence, but before I saw Memento I was reading Margaret Atwood. Cat’s Eye, The Blind Assassin, Oryx and Crake and Lady Oracle are all shuffle-structured books, although they tend to start at middle / beginning and finish at end / middle (whereas Memento starts at the beginning / end and ends at middle / middle). Orson Scott Card does a lot of shuffling within the corpus of The Worthing Saga, too; I actually read that in high school, so I guess it was really my first exposure to the style.
Of course, that’s omitting the randomly jumbled reruns of cartoons I watched as a kid, which seemed to come from different seasons at random–not that Thundercats drove a terribly epic tale, but the cast (to my perception) did expand and shrink on a daily basis. They weren’t doing it on purpose, though.
I’m not sure what single factor determines my fascination with these stories. My borderline ADD is certainly involved, which doesn’t imply a negative context: there’s something important and powerful about screwing with linearity, about building a narrative out of noncontiguous events. It makes individual elements of a story stronger, for one thing; there’s no room for laziness when every page has to give you something to take back to the larger structure. (Note that this is also one of the big reasons I like word-count fiction so much.)