A fairly common question on Tolkien discussion forums wonders why the Fellowship didn’t just fly into Mordor on the Eagles. It is frequently illustrated by the (in)famous How It Should Have Ended video:
The video is, of course, comedy, and not all Eagle scenarios are the same, yet it raises an interesting question. However, the reason the Ringbearer did not fly to Mordor by Eagle is fairly simple: the purpose of the Fellowship of the Ring and the linchpin of th entire strategy decided on in Rivendell was to destroy the Ring in a mission of secrecy.
Taking the Eagles might have worked, I will grant that. It may have been a successful mission and allowed the Ring to be destroyed earlier than it “actually” was. However, it would have sacrificed secrecy and drastically increased the changes of the Ring being captured. When you have the fate of the world hanging in the balance, you don’t want to take any unnecessary chances.
Eagles are, clearly, far more noticeable than Hobbits or other travelers on foot. We don’t know how exactly Gandalf planned to get into Mordor, but we can surmise that they would have gone through a mountain pass or valley some where. We know of only three (the Morannon, Cirith Ungol, and the Nameless Pass), but it stands to reason that there were more. Not ideal ones, perhaps (though Cirith Ungol itself was not ideal), but mountains are not impenetrable and continuous walls of rock.
An Eagle flying through the air would be easily noticed by Orcs or other watchers (remember the sinister and sorcerous ones at the Tower of Cirith Ungol – there might have been more). Travelers on foot could sneak around much more easily, scout ahead (especially with a ranger), and slip by unnoticed (remember how quiet hobbits are?). The Eagles might have been able to slip by unnoticed, but it would have become far more likely that they would have been caught. Once inside Mordor (if they even make it), there is still the chance that the Eagles could be caught. There are the threats of the Nazgul’s fell beasts, and archers (the Eagles in The Hobbit were afraid of shepherds with bows, so one can imagine how they might react to trained soldiers).
The “classic” Eagle plan, as outlined in the YouTube video, would not work for a couple of reasons. First, the Ring could not just be dropped into the caldera; it had to be taken into the Crack of Doom itself: the center of Sauron’s sorcererous powers. The Crack of Doom was at the end of a tunnel that bored into the mountainside, and an Eagle would likely not fit inside, so it would have to bring have a rider. This would limit the height to which it could fly (the rider would need to breathe) and its agility during a fight. Yet more possibilities for failure. Second, a giant Eagle landing on the slope of Mount Doom would be quickly evident to any troops stationed there. A small group of people on foot might be able to sneak up unnoticed. Again, the Eagle plan might work, but it increases the chances of being caught.
In conclusion, the Council of Elrond did not know exactly what to expect in Mordor, so they had to plan for the worst (i.e., assume the worst case scenario for each possible solution). The Fellowship plan was itself a very long shot and indeed, it failed in its original conception, though obviously a fragment of the Fellowship persisted. The Eagle plan raises such a host of potential issues and problems that I think it is quite understandable why the Council opted to send people on foot. As I mentioned at the beginning, their concern was stealth, not speed.