Indie comics writer Dirk Manning (Nightmare World) has a writing advice column called Write or Wrong. It's geared towards people trying to break into the comics industry, but a couple of weeks ago he ran an article called "Kill the Buddha" that's applicable to any writing endeavor. Or, part of it is, at least. Manning goes off on a lot of tangents about the nature and business of collaboration, but he eventually gets around to this helpful reminder:
"Do not seek to imitate the masters… seek what the masters sought. If you meet the Buddha… kill the Buddha. Your goal should not be to create comics as good as your favorite comics… your goal should be to create comics that are better."
Substitute "stories" for "comics" and you've got some great advice that crosses mediums.
I was at a convention once and got the opportunity to walk around it with one of my favorite cartoonists. He was looking for Jack Kirby stuff and I was surprised to learn that Kirby was one of his influences. His stuff doesn't look much like Kirby's (or anyone else's, which is why he's one of my favorites). I must've said something to him about that, because I remember that he told me that he wasn't wanting to draw like Kirby; he was wanting to achieve the same kind of effect that Kirby achieved. He was trying to learn what it was that he liked about Kirby's work, so that he could learn how to do the same thing in his own style.
When I think about my own literary idols (Neil Gaiman, Ian Fleming, Arthur Conan Doyle, and Edgar Rice Burroughs, for example), I can't get my mind around trying to write better than them. But I can conceive of studying their work in order to find out what they were/are seeking to accomplish. That's a hard enough task, but then the real work begins: trying to accomplish the same thing in my own style.