The one piece of writing advice you will hear over and over and over again? Read a lot.
It's definitely important. If you want to be good at something, why not study what other people have done before you in order to build off of it and make it new? You have to be a reader in order to understand what readers like. That's how you get more readers to pick up your books. It's simple, really.
People will tell you to read outside your genre, too. Don't just read the best of what you want to be but read everything you can get your hands on. Personally, I try to limit my intake of bad writing, but once I've started a book, I try to finish it even if I'm not crazy about it. Why? Because I can still learn something about writing from it. If I only read the first chapter I may not be able to put my finger on exactly what it is I don't like. If I read the whole book I can usually tell you exactly what it was I didn't like, and thus know what to avoid in my own writing.
The one thing that people usually don't mention when they give this type of advice is what they are actually reading. I'm going to tell you what I'm reading. In fact, in the spirit of it being "Best Books of 2011" season, I'm going to tell you all of the books I read in 2011. I read a total of 40 books this year, and I plan to break up the list into manageable chunks over the next 4 Wednesdays. I'll give you a few of my thoughts on each book so you can decide whether to add them to your reading list.
In the meantime, check out the NY Times list.
UPDATE: I recently found The Millions' A Year in Reading List which is similar to what I'm doing, but asks famous authors to name their favorite book that they read in 2011.