Wordpress.com allows you to create a free blog, but it will come with significant limitations (including limited storage and customization options). The WordPress software (which you can download from Wordpress.org) is 100% free. However, you'll most likely have to pay at least a little bit for a web hosting package (unless you happen to have an old computer you feel like turning into a server). There are a handful of free web hosting providers, but you'll probably find their service and features frustrating. If you're absolutely committed to creating a free WordPress blog, I would recommend looking into Amazon's cloud solutions; they have a free tier, and their rates are metered (and cheap), which means you'll only pay for the blog traffic you actually use. The one downside to Amazon is that it can be very complicated to set up.