SS got quite a bit of press a few years ago -- I'm surprised it's not mentioned more. It's 100% hosted (no free version or download). They boast "designer" quality templates and themes. And even the basic platform allows you to integrate a blog, static site and forum/community.
It looks like it appeals to folks who don't know squat about CSS, HTML, PHP, etc. and just want to focus on content. The upgraded version gives you access to the CSS (akin to TypePad's tiered offerings, if I recall correctly, except that SS doesn't offer a free version). But even with the basic platform you can insert your own HTML blocks (including ads), akin to Blogger. So it has that advantage over the WP hosted platform -- an advantage that you pay for, of course.
No, I'm not promoting it here. I looked at some featured sites built on SquareSpace, and many have a certain look and feel that I don't like personally. Most are fixed width and scroll off the page horizontally on a screen with fewer than 1280px, and the font-size proportions don't look proper to me. Too much emphasis on "design" and too little on usability for the greatest number of readers, IMHO.
It's funny how you can often tell the second you land on a site/blog whether it was built on WP, TP or Blogger. The same applies to SS.
Ahh... in general, fully hosted solutions haven't been discussed very much here for a variety of reasons. I think the main reason is that on a full hosted solution, especially a paid one, people go to the person they're paying and ask for help instead of coming to a forum.
Here at WebmasterWorld there are some big fans of fully hosted options like Wordpress.com or what have you, they just don't tend to post on this forum much.
As for the look - strange how that is. No matter how themeable a CMS is, there is often a certain look, though I feel that's evolving and it's becoming less and less obvious.