Boston taxi cabs are waiting at the airport 24 hours per day. We don't recommend the taxi cab if the destination is over 15 miles away because the cost is so much more than it would cost you to reserve private car service in advance.
You can take the MASSport bus from Hynes Auditorium to Logan (about $5 one-way). Its a luxury urban style bus perfect for travelers with luggage or not. Or you can take a Blue Line subway. At South Station you go to the Logan Express bus terminal level for buses leaving all day long.
The cabs charge fixed rates from Boston Logan Airport to a number of cities and hotels nearby, such as the town of Allston, the Seaport, Cambridge, Brookline, Dorchester, Roxbury, Mattapan, Children's Hospital, Somerville, Medford, the hotels, the hospitals, the universities. Flat rates are approximately $18 to $55.00 depending on destination. Wait time may be charged $28.00 an hour.