Well there is always Blogger of course, but Messy Christian highlights some other options like Wordpress and Blogs.com. Honestly Blogger has gotten a lot better over the course of the almost 2 years I've used it. None of the free sites have much draw for me.
In the beginning, it was unreliable and you could never be quite sure if your post would go through or if you would lose it when you hit the "publish post" button. Not so anymore. Sometimes Blogger still has trouble publishing, but I haven't completely lost a post in a long long time. I just have to try to publish later if the server is laggy.
The old comment system stunk and there was no way to do trackbacks. Now you can open comments in popups and there are provisions for anonymous commenting within blogger. There is still no way to do trackbacks, but commenting improved to the point that I will probably be switching back to blogger comments in my next template revision. Especially once I realized that Haloscan forgets old comments.
Blogger now hosts images too, which it didn't do in the begining. My days of having to find a free image webhost are over because Blogger does that internally now, but I still use photobucket when necessary.
Oh and there are good hooks for Google Blogads if you want to use your blog to acquire money and power. Unfortunately if I made money off my blog, I wouldn't be able to blog when I get bored at work.
All in all, I like Blogger right now. If I wanted to move to something better, it would have to be considerably better. And I would probably have to pay.