So, what do we have so far?
My old photo storage site now offer blogging platform:
There is also
http://www.insanejournal.com/ - concept similar to LJ
Blogger (blogspot) since some time ago started associate itself, in comment section and log-in, with Google - which, knowing Google reputation with censorship in foreign countries, isn't exactly encouraging. But the platform is there.
About two other popular platforms - TypePad and Wordpress: see here.
12/10: Thanks to 2Blowhards, I just learned about this great platform, Wordpress.com [not to be confused with WordPress]. Looks terrific, so far.