I've always worked hard with my drupal theme designs to make sure that each page has just one <h1> tag.  The front page should have the site title wrapped with <h1>s, and the other pages should have the page title wrapped with <h1>s (maybe having the site title in a large - but non H-tag - element).

Often, drupal themes as distributed require some hacking to make this work.  Unless a specific check is done in the processing for the site-title in the header section - to check whether a page is the home page - multiple H1 tags are likely. Zen has one way of doing this that I more or less follow; some other themes do it differently; some themes don't do it at all (and need hacking).

Interestingly, I had always thought it was a commandment to not have multiple H1 tags.  But I just ran across Matt Cutts's recent youtube explanation that multiple H1 tags aren't strictly forbidden.

Nevertheless, even in light of the video, I still think I'm taking the correct approach: just one h1 tag per page, which is the page title for all pages other than the front page.  By the way, I also specifically change the input filters for content on all pages to prohibit use of the h1 tag in all text.  (For anonymous users, the input filter is even configured to bar the use of any header tags in the text fields.)