I've taken photos at all three DC-area airports, and all offer a variety of good vantage points. As I just wrote to AirGirl in agreement with Rafal, DCA is the most photographer-friendly. You can get dramatic take-off and landing shots from Gravelly Point Park, which you must enter from the GW Parkway northbound. The new "crystal cathedral" terminal offers good close-up shots, but beware of window reflections.
BWI's observation gallery offers good shots of Continental, Southwest, and America West. There's an observation park on Dorsey Road (Rt 176) very close to the end of one of the main runways on the south side of the field. The neat Smithsonian Aviation Store in the Observation Gallery closed down, unfortunately, about a month ago.
At Dulles, there's a food court around the base of the control tower on the departure level that offers good shots over the old UAX gates. I don't know the perimeter roads but a steady hand can get good shots from the mobile lounges when the light's good. Now that international traffic at IAD is heavy, between 4:30 and 6:30 PM you'll find a good selection of foreign jumbos. BWI has the daily BA 763, Icelandair 757 and some Caribbean flights, but that's about it.
I don't know the area photo clubs, best of luck in finding the right ones.
Need a new airline paint scheme? Better call Saul! (Bass that is)