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I recommend TypePad because I use it myself, for my personal blog, and I've been happy with it since I started on it 11 months ago after my previous hosting company melted down.
Vox is operated by the same company that operates TypePad, Six Apart.
Vox is a good service if you want to limit access to some or all your posts.
For example, many parents are cautious about posting information about and photos of their kids; Vox lets you limit access to those posts so that only friends and family can see them, while less sensitive posts (like your opinion about the last couple of episodes of Lost) are viewable to anyone in the world.
(Those eps totally rocked, by the way.
I think that Juliet is actually working against the Others, don't you?
)
These are both good platforms for friends-and-family blogs, by which I mean online journals that have fewer than 100 readers.
These blogs describe what the author did and saw that day, photos the author uploaded to his Web site, and links to pages of interest elsewhere on the Web.
Sometimes a friends-and-family blog can grow into one of the most popular blogs on the Web., but that's more rare than lightning striking.
Mostly, friends-and-family blogs never get more than a dozen readers, and often their authors are quite happy with that.
TypePad will also host much bigger blogs.
It'll host commercial blogs with advertising and traffic-tracking tools and links to affiliate programs to generate revenue for the author.
Google ...