I saw this yesterday, and just had to pull over and grab a shot. As for the actual Addams family, the big joke of course, is that they (Morticia, Gomez, Fester, et. al.), really are ‘good people’. They are kind, generous, and truly family-oriented, without a hateful bone in their bodies.
Though he wasn’t created by Charles Addams, my favorite would have to be Cousin Itt. Here he is from the TV show, having traded in his usual bowler hat for a beret and glasses, presumably in a beatnik phase. I seem to recall that he liked to hang out in the chimney in his room, and would descend head-first through the fireplace.
Wikipedia says that in Italy, he is known as cougino Itt or cougino Coso.