The disappearance of 'ne' in 'ne... pas' is paradoxical, because
it's the most important part in the negation.
'ne' comes from the Latin 'non', which means 'no', while 'pas'
comes from the Latin 'passum', which means 'step'. The Romans used
to say 'non passum ire' to mean 'do not go one step',
i.e 'do not go'. This usage was extended to every kind of negation in
French, so that 'ne... pas' became the equivalent of the Latin
'non'. The speakers forgot the original meaning of 'passum', and,
nowadays, few Frenchmen know that 'pas' was not part of the negation 1000 years ago.
If a Frenchman says 'J'irai pas chez vous' and means 'I won't go to
your place', you may answer to him : 'Donc, vous viendrez chez moi'
(so, you will come to my place). He will stare at you with strange
Update after Gritchka's writeup below: what I said
about "pas" is true about other negative words in French. For example,
Michel Bréal gives a list of negative words that had positive meanings in
Latin or old French:
pas: Latin passum (see above)
point: Latin punctum (cf English "point")
rien: Latin res (thing)
plus: Latin plus
aucun: Latin aliquem unum (someone)
personne: Latin persona
jamais: Latin jam magis
Because these words are usually considered as negative, there is little
place for confusion, except with "plus". In written French, "j'en veux
plus" may mean "I want more of it" or its opposite: "I
don't want it any more". But the confusion disappears in oral French,
because the final "s" in "plus" is mute when (and only when) the word is negative!