Off the top of my head I know I've taken public transit to/from the following airports:
US Domestic:
-ATL (MARTA) (Both to downtown and also because there were times rather than paying to park at the airport, my father would park in a parking lot just inside Ft McPherson and then catch MARTA to/from the airport)
-JFK (Subway/AirTrain)
-LGA (Bus to NYC Subway and Regional Trains)
-DCA (Metro)
-ORD (CTA)
-BOS (MBTA)
International:
-LHR (London Underground)
-LCY (Docklands Light Railway)
-VIE (U-Bahn)
-TXL (Bus)
-CDG (Paris Metro)
-BNE (Train)
-OOL (Bus)
-SYD (Metro)
-AMS (Train)
-FCO (Train)