Basically you don't need Web Hosting for your own WordPress Blog. There are dozens of providers, which give you the opportunity to run your WordPress Blog without your own Web Hosting solution. This has some advantages like it is easy to set up and to use, but there are a lot of disadvantages too: designs are limited, configuration is limited and many more. The biggest advantage of a WordPress Blog which is not self-hosted might be, that the domain where your blog is published has already some traffic. But if you decide to start a self-hosted WordPress Blog, then getting some visitors isn't that difficult at all. All in all there are a lot of more advantages when you run your WordPress Blog on your own Domain.
The self-hosted solution for WordPress Blogs is far more flexible, than the one which is offered by WordPress and others. But not only the plus of flexibility and the freedom of choice in case of designing your blog are great pros for the solution based on self-hosting. With this solution you also have the chance to earn some money. It is not allowed to advertise for your own revenue on free blogs, but with your own WordPress Blog you can benefit from Google's Adsense, Yahoo's advertising and also from affiliate programs.
If you weigh up the pros and cons of the self-hosted solution, then you will see that this way is the only reasonable opportunity. Freedom, flexibility and the chance to earn some money with your blog are advantages that can never be made up by the other solution. Although you'll have to train your software skills to cope installation and maintenance chores, the self hosted solution is always the better choice!