I've used a few didfferent free blog hosts. You can't go wrong with Blogger, since that's so simple to use, and Adsense is integrated into it. There's Bravejournal.com, part of Bravenet. That's good. Can't put Adsense on it, though (at least as far as I know).

The best host I've used, though, is Blog-city.com. Unfortunately it's not free (anymore). But it's very good, very reliable, and the customer service is excellent.