While you can make use of Wordpress for free from their own site, and install it on any number of hosting providers, that can be an issue if you want to really grow and expand your site past a simple blog implementation. The issue is that Wordpress was created back in the day when elastic and scalable computing clouds didn’t exist.
The downside is that you have to plan and do a bit more work to get your site hosted. But the upside is that if you blog balloons, you don't have to mess with moving it over to a cloud provider.
Both AWS and Rackspace have attempted to rectify this situation with ways that you can create Wordpress sites on their clouds.