In the US? My experience is that most airports are not connected by railway or subway. Admittedly most of my trips were more than 10 years ago, but I would be very surprised if things have drastically changed. Yes, in Europe it starts to be become rarer that major airports have only bus connections.
There's probably no more than twenty airports in the US with rail/subway connections. Notably the second busiest (LAX) does not have a rail connection but they're finally building one.
Boston, Cleveland, Chicago O'Hare, Chicago Midway, Providence, JFK, LGA, Newark, Philly, BWI, DCA, Atlanta, SFO, Oakland, Denver, Fort Lauderdale, Miami, Portland, Seattle, Dallas/Fort-Worth, St. Louis, Minneapolis/St. Paul, Milwaukee, Salt Lake, Phoenix.
If you include proposed or in construction links, there's also Honolulu, Washington Dulles, Orlando, LAX. There's also a few more airports that have bus service to the light rail line (e.g., San Jose airport).
Essentially, every city with a subway system has a stop at the airport, LA and San Juan being the two exceptions here. Some commuter rail networks stop at the airport. Several light rail systems don't stop at the airport, particularly if the airport is well out of the center of town. So it's more of indictment of the degree to which US cities lack rail transit.
