Slouman, I was in a taxi today so took the opportunity to ask the driver about the rough cost from Black Falcon Cruise Terminal to Logan Airport. He estimated the total cost (excluding tip) at $15-$20 depending upon traffic. This is per taxi, not per person. Note that an airport fee of about $3 will be added to what's on the meter. I included this fee in the above estimate.
Now, for those going in the opposite direction -- from Logan to the Black Falcon Cruise Terminal -- the fare will be much higher, closer to $30 according to the driver. That's because there are very steep fees imposed on the airport taxi pool as well as a hefty toll for a tunnel that runs from the airport.
The shuttles poormom mentioned are typically used when Boston is a port of call (not a disembarkation point), and don't go near the airport. My guess is that these are also used by the cruise lines for shuttling pax to the airport, at a fee that very likely exceeds the cost of a taxi. It is still a wonderful convenience for those visiting Boston for the day by ship.
Any further questions, please let me know. I work in Boston and have been to both the cruise terminal and airport many times.