You definitely need to read a lot...and honestly, you need to read WIDELY. That means everything from genre sci-fi to short stories about a rock; you do this simply to see what works and what doesn't. Magazines, movies, books, short stories, newspapers, these are all good ways to enhance your writing in different facets--but you should never limit yourself to just one part if you want to be a decent writer.
agree, and disagree (but more agree, i think)
you're absolutely right that you need to read a lot, and to expose yourself to a variety of influences (I believe watching good films, good television, reading non-fiction, following (non-celebrity related) current events, all contribute to improving yourself as a story teller).
But I can't quite swallow the notion that you need to read from every genre. We all have our preferences, (and I'm not stupid enough to get into a debate over which are more valid) and I don' think it's essential to force yourself into reading things that fall massively out of your field of interest.
(of course there's an argument that it's still valid to read things you don't like in order to understand why you don't like them, but I think life's too short—better to invest your energies on grasping why you love the things you love)
There are writers, and even whole genres, that have no appeal to me. I'm not going to read shit*, just to broaden my horizons.
*'shit' being determined entirely based on my own opinions and preferences. Everyone is free to formulate their own individual definition.