Who knows any free bloggin platforms, which google respects, for example wordpress.com will be the first in this list
you should go for individually installed blogs with individual domains.. hosted blogs are not respected any more..
I've had pretty much good success with wordpress.com. I've setup 3 wordpress blogs, all unique content and 2 of the sites got indexed quickly and PR3 at the next update. The downside of having a blog at wordpress is that you cannot setup a 301 redirect once you opt to move away. You can get trickel of traffic via your links though - that's still an option.
It's like saying Google doesn't respect Gmail at the moment For best SERP results I would go for my own domain and host. SEO Hosting + GoDaddy do wonders and give you much more control.