IE is supposed to support it. They just released a preview last month. Safari and chrome are there. Just leaves firefox who I imagine will be on it.
There is no logic behind the favorite between Google and HTML5. I do not think Google will give any favor to it personally. There are many suitable factors to be counted towards site ranking more than just a HTML version.
If by favoring you mean giving preferential weighting in search engine results, purely on the basis of the version of HTML used by the site, I doubt it. Is there a precedent for this? Did anyone prove a link, say, between HTML 3 and 4 and search engine ranking for a given site?