The site I'm making - and as a lot others do - has a unique homepage, which is more like an index to the site than a part of it; imagine an exclusive (and loud) layout scheme, elements, content, all of which further links to the content part on my site.
Since the homepage makes itself so evident, is there a need to sacrifice pixels and visual flow for a strip of breadcrumb that is only gonna say "Home"?
I would tend to mostly agree with most who have already commented on your question in that breadcrumbs serve no purpose on the homepage.
Besides the resource already mentioned by @Brian above, baekdal.com includes a relevant point:
Front page breadcrumbs are often a mistake because it only contains "Home" - it is not even linked. Your visitors will most likely be confused about this single word, and not get the idea before they visit a sub page.
Breadcrumbs are a trail back to the homepage, and since you're already there (and you've mentioned it's obvious where you are), it would just be another redundant link to the same page -- taking up unnecessary space.
Note: The one case you could possibly argue for (although not a very good point) is that all sub-pages may have breadcrumbs and thus the layout could be considered inconsistent by not having the same bar on the homepage.
