Most web designers are completely oblivious to SEO. The Joomla default template, for example, doesn't use <h1> at all, it uses <div class="componentheading">. "componentheading" has no SEO value.
Using <h1> for the site name is a complete waste -- except on the index page.
There should be one <h1> tag and it should be used for the page title. W3C agrees with me.
<h2> should be used for paragraph headers, and those should be rich with related keywords.
Sidebars and other site-wide elements should not use <hX> tags, they should use CSS tags for styling purposes.