The closest in the existing system is in the Users > Roles menu in the Dashboard, you can give permission to the "Authenticated" user to "Publish or unpublish own blog post". You can create a blog owned by that user, but I'm not sure if that would mean
they can still post to any blog. The Blogs permissions perhaps need granularising a bit so there are "Publish to own blog" and "Publish to any blog" options.
To have it so a blog is automatically created for a user, or so they can create their own blog (but only 1 of) requires some modification. I was looking at doing a similar thing for a website I'm working on, but I'm not yet sure if it's required - I've looked
into doing it but haven't started anything.
You could probably do either of these things by creating your own module rather than editing the existing blog module to avoid breakage as 1.1 approaches - although if you made a modification to Blogs itself you could try submitting it as a patch.
First you should play around with the existing blog and roles functionality to see what it does, and also the recent posts widget (which unfortunately will only display posts from one blog for each instance). I'm happy to point you in the direction of where
to look for relevant code, but familiarise yourself with the system a bit first :)
There is also a Profiles module available which will give each user a profile page that will go part way to what you need.