There’s a prevailing fan theory out there that in The Lord of the Rings, Gandalf had a secret plan to get the Fellowship of the Ring into Mordor by using the eagles to fly there. The best version of the theory goes like this:
After passing the Misty Mountains, Gandalf planned to make contact with the eagles in order to recruit them to carry Frodo and maybe a few others to Mordor, maybe all the way to Mount Doom itself. He told no one of this plan so that if they were captured, they couldn’t reveal it.
Once the Ring was airborne, Aragorn, Boromir, Pippin and Merry would have gone to Minas Tirith. Using the palintir of Denethor, Aragorn would have revealed himself to Sauron. This, combined with the knowledge that two Hobbits of the Shire, the last known wielder of the Ring, were in Gondor, would have gotten Sauron to launch an all-out attack, leaving Mordor virtually unguarded and open to entrance by Frodo and the eagles.
The cherry on this theory is that Gandalf’s last words before he's dragged into the pit of Moria are “Fly, you fools!” He was trying to give the plan away. Some people love this theory; some people say it wouldn’t have worked because Gandalf was in no way the brilliant mastermind people think he was (the whole reason they had to go through Moria in the first place was that Gandalf delayed leaving Rivendell until winter was upon them and closed the mountain passages, and then he gets himself killed basically because he stopped to read a book in the middle of the adventure). I say both. Using the eagles was Gandalf’s plan, because he was an idiot.
First things first: the diversion. Aragorn is a vagabond ranger from the north coming basically to usurp the rule of arguably the most powerful non-magical entity in Middle Earth. In a city that, by the way, he had kind of a dubious claim to even if they believed he was the heir of Isildur since Aragorn’s descendants were the kings of Arnor, not Gondor. In fact, they’d tried in the past with a much better claim to ascend to the Gondor throne and failed.
So a big part of Gandalf’s plan is assuming Steward Denethor is just going to hand over power to some dude with an old sword in the middle of the biggest conflict of the age, as well as the use of a powerful magical artifact that could give Sauron direct influence into the city. Let’s not forget that the only reason Aragorn’s final ascent to the throne was so bloodless on the good guy side was that Denethor went mad and burned himself alive. Banking on a peaceful transfer of power to Aragorn was monumentally naive and ridiculous.
Now let’s look at the eagles. The movie versions suffer from a bad case of Third Act Geographic Smushiness Syndrome, so it’s forgivable if the sheer scale of Middle Earth is murky in your head. However, the path that Frodo and Sam took from Lothlorien to Mount Doom is 859 miles long, or about 41 percent of the distance between the east and west coasts of the continental United States. Even taking a shorter route over air, it would still be a very long way to fly carrying full-grown people or even Hobbits, plus provisions.
Plus, there’s no promise it would be safer. The eagles themselves are not generally beloved by everyone, and say in The Hobbit that they have to avoid settlements so as not to get shot by shepherds and the like. On top of that, it’s pretty well established that Sauron has airborne spies of his own, so in a way they are even more likely to be spotted.
This is presuming the eagles even agree to do it in the first place, and there’s no indication that Gandalf had the faintest idea where he would find the eagles to even ask them. His fellow wizard, Radagast, might have arranged it (as he arranged an eagle to bear tidings to Isengard, where Gandalf was found and rescued), but one of the things we learn while waiting to depart Rivendell is that scouts had tried to visit Radagast and found his home unoccupied. How was Gandalf going to get his eagles in the first place?
So yes, I think Gandalf’s plan was to take to the air, and I think the reason he didn’t tell anyone else in the Fellowship this plan was that he knew it was patently ridiculous and almost certainly wouldn’t work. Bear in mind that the entire war is resolved because Frodo got his finger bitten off and Gollum tumbled into lava doing a happy dance, and that was actually the best-case scenario for the entire thing. Just one more case of the little people Gandalf gets in trouble coming through by chance at the last minute when every one of his stupid, stupid ideas fails to pan out.