Free website services that are useful, useable and reliable.
Blogger (blogger.com). Lightweight and simple. Works well if you have a gmail account as they're a subsidiary of Google.
Wordpress (wordpress.com). An independent blogging service provider with both free and paid-for offerings. Very fully featured with a focus on addressing the needs of dedicated bloggers.
Weebly (www.weebly.com). A freemium model. Free basic, pay for upgrades.
There are many many other service providers and approaches.
In addition you might go the route of registering your own domain name and then pay for it to be hosted by a third party hosting/application service.