While flying, how do I contact someone who is on the ground? As a regular General Aviation pilot, how do I contact or relay a simple message to someone on the ground? For example, to update a friend, family member, or taxi company with an ETA or a meeting point. Assume that asking them to follow a tail number on something like FlightAware would not suffice.

Cell phones are not an option. FAA AC 91-21.1B prohibits cellular communication while in flight (Correction: see comment below; it's really the FCC that prohibits cell use), and cell reception above 5000ft AGL is pretty poor. 

Commercial operators have access to more sophisticated services like ACARS, ARINC, or satellite communications, but these are usually too expensive or complicated for the regular GA pilot.

Can Flight Service Stations (FSS) call someone and relay a short message for me? Has anyone tried this?
Once, in a pinch, I persuaded Phoenix Approach to call my mother-in-law and advise her to meet me at an alternate airport since I would have had to hold for two hours to get into PHX where we'd originally planned to meet. This is definitely not something that ATC does on a regular basis.

Other options include carrying an Iridium handheld satellite phone (not cheap, but certainly a possibility for light GA) or installing an amateur radio transceiver.