I think the best place to put breadcrumbs is in the trash. They don't really provide that much value to a site.
If you insist on having them, then after the site navigation is the best place to put them. Putting them at the very top of the site is a VERY bad idea to me. It's going to hurt your SEO and accessibility for sure, and it is also likely to hurt the aesthetic of your site. Breadcrumbs aren't exactly "pretty".
The reason that they are put right above the content is because they relate directly to the content. Putting them above your navigation/header breaks that link with the content and the breadcrumbs lose some context. I've seen this sort of thing referred to as cognitive resonance, although that really isn't a valid phrase, it kind of makes sense here.
EDIT: Expanding on how it hurts accessibility and SEO:
Accessibility: If you put the breadcrumbs at the very top of the page, people using assistive technologies like screen readers now have to move through all of your breadcrumbs in order to get to the site navigation links. Because of this, you need to really consider what the more likely target is for your user, clicking on a navigation link or clicking on a breadcrumb link. Unless you are Craigslist, where the only navigation you have is breadcrumbs, the more likely candidate is the navigation links.
SEO: Search engines only follow a certain number of links (and read a certain amount of content on a page, but that's less important here). Again, it leads to importance. What is more valuable for you to have followed by Google's crawler, your breadcrumb links or your main site nav links (which will ideally lead the crawler to much more content than the breadcrumbs will). Now, this is probably less of a concern, because most crawlers will probably follow deeper into the page than just your navigation and your breadcrumbs, but it's better to be sure with that sort of thing.
Also, thought of another reason to not put them at the very top of the site: Not every page on your site is going to have breadcrumbs. As such, the user will likely become used to your header looking a certain way and will learn to ignore it over time unless there is a specific action they want to take there. This means that your breadcrumbs are likely to get ignored even more than if they are right above your content. At least if they are above your content, they are more likely to be in the user's vision as he reads the content (again, the resonance between breadcrumbs and content).