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Every web page should have a HEAD and BODY tag, but some people, erm, forget them. What happens if your BODY tag or other significant tags are missing? Will search engine spiders ignore the web page?
Both tags are optional. The big issue is more that Googlebot may not know how to distinguish between the HEAD of the page and the BODY of the page if the code snippet is missing.
In general, though, if your page does pass HTML validation, the crawler should have a good idea of how to traverse the page and get the content. And if not, and there are some missing close-tags, some portions of the web page may go unnoticed, but it's not 100% definitive.
A test is ongoing to see how a missing BODY tag will impact the crawlers in the related discussion at WebmasterWorld.
