What are some practical uses for the Quaternion? Why not just use the Euler X, Y, and Z axis rotation values?
It's not intuitive how one should manipulate Quaternions. Can someone explain this?
Quaternion has the advantage that it gives better interpolation between keyframes for arbitrary rotations, compared to
axis-angle, this is often used for character animation and why its default for armatures.
It also avoids the gimbal lock problem.
You make a good point that the f-curves are hard to control. Typically you wont manipulate each axis them directly, and instead pose the rig in the viewport.
So for walk cycles and arbitrary motion, quaternions are fine, Euler's are better if you want to control each axis and are animating something which inherently has separated axis you would want to apply in order (robotic joints for example - a gun turret where you might want to control 2 axis directly).
For more general info on this topic see: