I hear this question thrown out so much.
Based on Tolkien further elaboration of Middle-earth in his other books, the Eagles were very independent race and preferred not get into the affairs of the other races, just like the Ents. They fly high in the sky, in high mountains and trees. Sauron's affairs and conquests mean nothing to them and will never affect their daily lives. However, Gandalf was a good friend of them, and whenever his life was in great danger (on top of Saruman's tower, or the battle in front of the Black Gate) they came to his aid, ONLY to save his life.
Another possible reason: Would you, as an eagle, want to fly a 150-200 pound person on your back all the way from Rivendell to Mordor? The distance covered is about 40-day walk.