This was never completely resolved, but it has been discussed quite a few times in the past.
Ulmo posed the same question in 2001 in
The Great Eagle Mystery; then it was asked again in 2002 by
Keeper of Dol Guldur in
Are they all stupid?. It arose again this year with a thread started by
Sardy, entitled
Gandalf/Eagle -> Ring -> Mt. Doom?, and we touched on the subject in 2004 when
Magician of Nathar started a thread called
Flaws in Lord of the Rings... Yes in the book. In this last thread can be found
my most recent opinion on the subject.
There's also rather a good argument for posting on the aforementioned threads
here.
All other arguments aside, wouldn't the story have been a trifle dull had the Eagles carried the Ring to the fire?