Cigars and Celebrations
I’ve never really known when or where the celebration cigars ritual originated, but I did find a thread on the discussion boards at StraightDope.com that provided some background on the tradition of giving out cigars after the birth of a child:

It seems clear that what began as a tradition for celebrating the arrival of a new child, naturally came to symbolize other momentous occasions in society. (I bet their celebration cigars back then were Cuban cigars, too.) And although this “shared bonding experience,” can be witnessed simply by walking into any busy cigar lounge, the opportunity to share cigars following life-changing events seems to suggest a much more liberating experience, especially for those in the group who don’t usually smoke cigars. It is in this context in which the following quote from the writer above is most apropos: “The gift of a cigar has always bespoken the donor’s ‘share my happiness,’ and the intrinsic meaning of this gesture has not changed.”
Being a cigar smoker, I get a kick out of seeing those who normally don’t smoke cigars partaking, say, at a wedding, or when a sports club has won a major victory. Sure, some of the cigars don’t get finished, which is a bit frustrating for someone like me, especially if the cigars are Fuente-Fuente OpusX or Padron Anniversary’s. But during that window of celebration cigars rule the day, and will hopefully continue to do so for generations to come.