I recently looked up the origin of "mooch", and the root of the word is apparently very, very old:
Whatever the distant origin of mooch, the verb *mycan and its cognates have been part of European slang for at least two millennia. [Liberman]
Are there other known words with origins this old? What current word has the oldest origins?
EDIT: I should specify that I mean traceable origins. I'm sure there was some word for "fish" being used since the dawn of language. I am not a professional, so I do not know the terms for this, but I imagine there's some form of measurement for the strength of links.