Note: I have just made this decision (March 6th, 2006), so much of my writing up to this point has been filled with the presciptivist nonsense of "he" and "he or she." From now on, I will attempt to use the more reasonable "they."
"Amoken" pointed me to this article about "their". I found it woefully short on references, so I followed the only link to this really nice article about grammar in general that mentions the whole "their" thing in passing... but does not even mention the "their was once correct" story.
I googled a quote from the first page, and found this site on gender and the English language, which refers to "they" as being traditionally used as a gender-neutral singular third-person pronoun. The claim is that "he" was introduced as gender-neutral in order to get rid of the usage of "they," although the article doesn't specify if the purpose was just for acts of parliment, or was meant to be a general prescription for all usage.
As always, wikipedia comes to the rescue: The Interpretation Act of 1850 was written to simplify the language. This was later ammended in 1978, which further stated that words in the plural also include the singular, and words in the singular also include the plural.
Although, we are not fully rescued by wikipedia, because it mentions nothing about the "their" issue, and doesn't even include the relevant quote. So, I looked further into this Act using google... and found nothing.
So, I googled around and found this gem. Exactly what I was looking for! this sub-page deals with more sources.
(Update Nov 2016: Those last two links are dead now, but it looks like that site has been moved to pemberley.com. So you can see the above instead at this site, although it looks like the more detailed sources are missing. sigh.)
So, "Everybody loves their OED/Jane Austen/Oscar Wilde/Shakespeare/King James Bible"