I can’t find any definitive proof online that says you need to use Heading Tags (H1, H2, H3, H4, H5, H6) or that they improve rankings in Google, and I have seen pages do well in Google without them – but I do use them, especially the H1 tag on the page. For me it’s another piece of a perfect page, in the traditional sense, and I try to build a site for Google and humans.
<h1>The Hobo SEO Company, Scotland</h1>
I still generally only use one <h1> heading tag in my keyword targeted pages – I believe this is the way the W3C intended it be used – and ensure they appear at the top of a page and written with my main keywords or keyword phrases incorporated. I have never experienced any problems using CSS to control the appearance of the heading tags making them larger or smaller.
I use as many H2 – H6 as is necessary depending on the size of the page, but generally I use H1, H2 & H3. You can see here how to use header tags properly.
How many words in the H1 Tag? As many as I think is sensible – as short and snappy as possible usually. Aaron Wall at SEOBook recommends not making your h1 tags the exact same as your page titles, although I personally have never seen a problem with this on a quality site. I also discovered Google will use your Header tags as page titles at some level if your title element is malformed.
As always be sure to make your heading tags highly relevant to the content on that page and not too spammy, either.