Airports can often be a form of Cul-de-sac's that can be difficult to service with transit. If you look at most of the airports currently served by or to soon be served by rail transit such as Salt Lake City or Denver, you will see a design that is basically a Cul-de-Sac: you have travel to it from one direction but you have to turn around to get out of the complex.
Last week I flew into Portland and took their excellent light rail service from the airport however, Portland is a perfect example of this principal. The Red Line ends at the airport and without a major reconstruction of the airport and/or the line itself, the line can never reach beyond the airport terminal itself.
This is true of many of the cities that currently have rail service to their airports including Philadelphia, Portland, Chicago (O'Hare), the new line to Denver, the future extension of the Washington Metro system to Washington Dulles, Baltimore and St. Louis. The Airport TRAX line in Salt Lake City will also be a dead end line.
There is a couple exceptions to this rule which includes the SeaTac in Seattle and Chicago-Midway (although both currently end at the airport stations there is planned extensions of both routes). However both of these stations are located at the far end of the parking lot and customers face a long walk to the actual airport terminals. I rode to SeaTac yesterday and despite the fact I walk a couple of hours a day, walking with luggage from the Link station to the airport terminal then to the respective gates can be a grueling experience.
The one exception to the above is Ronald Reagan Airport in Washington where the Washington Metro system is able to service the airport terminals and then continue on.
One of the worst example of providing service to an airport is the San Francisco BART line. First have the line to the airport plus a line that serves the vitally important connection to Caltrain at Millbrae. However, neither station has performed to potential due to the way the lines were designed.
As Jarrett pointed out, trains can either serve the airport, then reverse direction and head to Millbrae, or they can split with one train serving Millbrae and another the airport, or you can have option 2 with a shuttle between the two stations. Every time the schedules change at BART they seem to try something new and nothing seems to work.
Airport lines can provide a important multi-model connection to major airports. However, transit systems must also take into consideration if they are serving a cul-de-sac and whether those precious dollars could be better used for a line that can be expand to more areas in the future.
