I am having another geek moment again. Ever heard of negational verbs? They are the fabbest thing ever. Imagine the word "not" as a verb. Impossible? Even in French, I came to realize there is a potential for such things to arise when we say "Peut-être que non." (meaning "Maybe not."). Normally, que is used to introduce a relative clause, equivalent to English "that" or "which". So having non in the section of the sentence where a verb is expected implies that non here actually is meant to signify "it is not". Hence "Peut-être que non." equals "Maybe that it is not." Modern English employs a modal do to help convey the negative in conjunction with not... so in effect, don't may be in a vague way a kind of "negational verb", no?
Negational verbs are more overt in some languages like Finnish where ei is used to convey "not". An affirmative phrase like menen "I come" becomes en mene "I don't come", or perhaps rather "I am not (who is) coming." The ending -n marks the 1ps and as you can see it migrates to the negative verb when it is present. This can be traced all the way back to a negational verb *ei in Uralic. Here it is considered a verb because it takes the pronominal endings which are normally only used for verbs.
The reason why I have been thinking about this a lot lately is because of Indo-European grammar. At the University of Texas Winfred P. Lehmann's views are explained but I disagree with them. It's tempting in an SOV language to expect that the negational element should always be at the end of a sentence but there are other alternatives.
I was thinking of a negational adverb, not particle, in IE's earliest history. It works like this. It is similar to what we see in Uralic but Old Indo-European *nei would be rather a negative verb used to modify the main verb. On its own, *nei would have meant "to not be (true)". In effect it would be like saying "I go." in the affirmative and "I not-truly go." in the negative. Since adverbs tend to be preposed to the verb in natural SOV languages, there's no strong need to expect that *nei was once at the end of the sentence. Open your mind to fresh possibilities, people! Anyways, over time, *nei would erode into a particle *ne, still preposed to the verb like other adverbs until IE finally fragmented into the various branches we recognize today.
 (June 11/07) I found an inspiring pdf online called On the Diachronic Development of Negation [pdf]. It discusses the numerous strategies for negation in languages as well as the development of negational adverbs! I guess it's far more common than I appreciated and it adds some more crazy twists to my theory above because, for example, if multiple negative elements can come to be used to mark the negative in a language without being understood as a double negative (eg. French ne...pas, ne...guère, etc.), then maybe there was a double negative like we see in French used in a very, very remote ancestor of Indo-European. In varieties of colloquial Canadian French, pas has already taken over and ne is no longer added (eg. J'sais pas for Je ne sais pas). I also forgot about gems like the use of Italian non which comes straight from Latin adverb non.