Probably the single most important character trait for a writer. You need to be able to persist through writer's block, through dry spells, through self-doubt and family-and-friends' doubt, through rejections and contest losses and sudden and ill-timed changes in what the market wants to read.
2) A Thick Skin
If you're going to get down in the dumps and quit writing or querying every time you get rejected, or even every time you get rejected after you were given reason to get your hopes up, it's going to take a very long time to get to the finish line. Not everyone is going to like what you write, but don't let that slow you down. Keep writing, Keep submitting. Keep moving forward.
I took a class with local writer Katrina Kittle a while back. In past lives, she was a dancer and an actress. She said those careers, which include a LOT of rejection, were great preparation for being a writer.
Learn to repeat this little mantra: "Not my audience." Just like people don't all like the same food or the same clothes or the same television shows, not everyone likes the same kinds of books. (Some people don't like any books at all, but they're barbarians who would destroy civilization given the chance.) The fact that someone doesn't like your book doesn't mean you're a bad writer, it just means your book is not for them.
3) A clinical eye
In order to get better, you first have to realize you suck. Until you're willing to set aside your ego ("Look at this marvelous thing I've created!") and really see your writing for the flawed exercise it is, you're probably not going to get any better.
4) A love of reading
I frequently hear the following from people who have just learned that I'm a writer: "I've thought about writing a book." I just smile and say, "I think you should." Then afterwards, get back with me and tell me how it went....
The people that fascinate me are the ones who say this but are not themselves readers. How in the world can you expect to create something that you don't know anything about?
Read in the genre you want to write in--it will help you understand the expectations of your prospective readers. Read in genres other than the one you want to write in--it will give you fresh perspective. Read craft books. There are a lot of tricks of the trade that aren't apparent to readers. A few fortunate souls are born instinctively understanding things like point-of-view and plotting, but most of us need to be taught.
4) A love of writing
If you truly want to become a writer, you will spend a lot of time sitting in a chair in a room by yourself. According to Malcolm Gladwell, it will be something in the region of 10,000 hours to become an expert at anything. Or, to put it another way: your first million words are just practice.
Once you've gathered together these character traits and experiences, we'll talk about that MacBook Air.