When you're writing you're either doing it with your right hand or your left hand or both. Before you raise your eyebrows questioningly please remember that everyone uses both hands when typing on the keyboard. Other than that we all have a preferred hand to do everyday stuff, including writing.
Most people are right handed, thus belonging to an estimated 70-90% of the world population who are right handed too. There is actually no prevailing theory on why there are more people who prefer their right hand though. Sociological, biological and environmental theories try to explain this. Emphasis on trying. Of course, what most of us will have heard before, is the theory that links motor skills of the body to sides of the brain, often marking left handed people as the more creative and right handed people as the more practical ones. Besides the fact that some well known authors were left handed, such as Lewis Carroll, Mark Twain and H.G. Wells, this doesn't mean that right handed writer's were (or are) any less creative. The left handed ones simply stand out because left handedness is rarer. So, this theory leaves a lot to be desired and in the end it doesn't really explain the reason why there are so much more people who are right handed either.
Apart from people being either right or left handed, they can be mixed handed or ambidextrous too. Mixed handed, also known as cross dominance, refers to a person who can do different tasks better with different hands. Though this handedness is often neglected as we usually declare the hand with which we write our predominant hand. Then there is the rare ambidexterity which means that a person can do any task equally well with either hand.
If you asked me now what kind of handedness I claim my own, I'd say right handedness with a tendency towards mixed handedness. While I am writing with my right hand, I do prefer using my left hand for a number of other everyday tasks. Then again, I think a lot of people do, they just don't think about it consciously, thus would never get the idea that they are more than simply right or left handed.
In the end I guess you can't just throw people into one category or the other. Besides, even if you declare yourself either right or left handed, we should not forget that our two hands actually work together in very subtle ways. For example, for a right handed person the left hand is involved in important ways too – it orients and grips the paper, sort of the right hand's little helper. And these days – getting back to the initially mentioned keyboard – we sure give our hands equal rights when it comes to writing. At least I know of no person who'd only type with their right or left hand. Maybe our computerized lives push us towards ambidexterity, and if it does, it sure gives those researchers even more to ponder.