Is it possible to use the animals that are summoned using Conjure Animals as mounts?
As an example: Summoning Giant Eagles to carry a group up the mountain or over a wall.
Yes. The fact that the creatures were summoned makes no difference. The creatures are, by wording of the spell, also bound to obey any verbal commands of the caster, which will make them very reliable for such tasks as well.
As Slagmoth points out in the comments, however, the spell doesn't provide a saddle. Saddles are mentioned in the Player's Handbook, page 155 under Mounts and Vehicles:
Saddles. A military saddle braces the rider, helping you keep your seat on an active mount in battle. It gives you advantage on any check you make to remain mounted. An exotic saddle is required for riding any aquatic or flying mount.
Emphasis mine. So yes, a conjured mount will be equally capable of flying your party over a wall, but you need an exotic saddle for the job like you would with a non-conjured beast, unless you choose to summon a non-flying, non-aquatic mount in which case there is no RAW requirement for a saddle.