Blogger.com will let you use your own domain name and so will newcomer Weebly.com. If you’ve got free hosting credits with GoDaddy.com, you can use a credit then modify the domain to point to one of these free services.
Weebly actually lets you do a lot more than just blog. You can also create static pages a la WordPress.
Update: I’ve also found: jimdo.com (not free)