My experience was pretty classical at first--started with abridged fairy-tales (Illustrated Classics series) when I was four to five-ish. 'The Little Mermaid' non-Disney story disturbed me at the time, even in the children's retelling. Still does, actually. But I distinctly remember receiving The Hobbit for Christmas when I was five, though I didn't actually read all the way through it for another year or two. Read through all three books of The Lord of the Rings when I was eight, then The Lion, the Witch, and the Wardrobe. Flew through the rest of the Narnia books after that.
Let's see--I read lots of Enid Blyton (lashings of it, as she'd probably say), some Edith Nesbitt, George MacDonald's The Princess and the Goblin and The Princess and Curdie--I'm only mentioning the most influential books for me here. Then I decided I knew enough to write my own fantasy novel.
Didn't really get into sci-fi until I read Orson Scott Card's Ender series several years later (wasn't too keen on H.G. Wells as a youngster,, though I did like Jules Verne). That and some of Andre Norton's works. Oh, and Star Wars and the original Doctor Who, of course.
Anyway, those are my fantasy/science fiction roots. I might have left out one or two other major ones--if I remember, maybe I'll quote my own post later and add a postscript. (Pun totally intended.)