Most SEOs know that H1 tags are very important for search engines. In fact, H1 tags are next in importance for SEO after Page Title tags. H1 tags give you a short summary of the page contents. Theoretically, there should be one H1 tag per page only.
Google's charming spokesman for web design community Matt Cutts stated that in theory there should be only one H1 tag per page. And it makes perfect sense. How many summaries of one page should you have? However, in practice, there are situations where you can end up with several H1 tags per page. For example, most websites have a blog list page where many of your blog posts are parsed and their summaries are listed one after another. Since each of the blog posts have their own H1 tags, the segregated list page that gets parsed by a content management system ends up with multiple H1 tags. Sure, you can decide to use H2 tags for all your blog posts instead of H1 tags to avoid multiple H1s, but this might lower your SEO value, especially if you have many blog pages. You will end up losing a lot of your H1 tags in total.
And there are other situations where you legitimately end up with multiple H1 tags. In addition, some web owners don't know much about SEO, so they use H1 tags for all types of headers (first level, second and third!) simply because they like the style settings for this tag, i.e. its color, font and size.
It is not surprising, therefore, that Matt Cutts officially stated that there is no penalty for multiple H1 tags on a page. He also added that web designers should not go overboard and have dozens of H1 tags per page, nor should they include a whole paragraph inside the H1 tag, in the hope of getting more SEO value.
In other words, like with everything, moderation is key. Don't try to be perfect but don't try to be smart either. Select the middle way: create one H1 tag per page when you write content, but if you have pages on your website where content gets segregated from other pages, don't worry about your multiple H1 tags, so long as you don't have hundreds of them and they are not longer than one sentence in length.
Oh, and don't forget to include your most desired keyword variations in all of your H1 tags. It follows naturally that there are no restrictions on multiple H2 and H3 tags, since they represent sub-sections.
